Focus On Maths Grade 7

Applications of this chapter Statistics is a mathematical field that involves collections of data, compilation, recording, representation, interpretation and data analysis until a conclusion is made. Statistics is widely used in field of astronomy, economics, science, geography, sociology, business and many more. How do we get data from a group of people with different characteristics and races? How to record data systematically? 7STATISTICS 236 ©Praxis Publishing_Focus On Maths

Concept Map • Data • Qualitative data • Quantitative data • Statistical questions • Categorical data • Numerical data • Frequency table • Bar chart • Line graph • Pie chart Key Terms Learning Outcomes Learning Outcomes • Understand the concept of data. • Classify data into categories. • Understand the concept of frequency. • Represent data in frequency tables, bar charts, line graphs, and pie charts. • Find the relationship between data and bar charts, line graphs and pie charts. • Interpret data from bar charts, line graphs and pie charts. Ronald Fisher is a British mathematical statistician that pioneered the application of statistical procedures in the design of scientific experiments. Fisher summed up his statistical work in Statistical Methods and Scientific Inference in year 1952. Maths History Qualitative Data Diagrams Quantitative Data Frequency Tables Bar Chart Line Chart Pie Chart Data Collection Represent Data Interpret Data Statistics Primary Data & Secondary Data Types of Data 237 ©Praxis Publishing_Focus On Maths

238 CHAPTER 7 Statistics Flashback 1. Fill in the blanks. (a) 100 × = 360 (b) 72 × = 54 (c) 690 ÷ = 23 (d) 690 × = 23 How will you present the data obtained from the data collection in a graph? According to the 2020 census by Statistics Indonesia, the total population in Indonesia is over 270 million. With more than 300 ethnic groups, the largest ethnic group is the Javanese who make up 45 percent of the total populations, followed by Sundanese (14%), Madurese (7.5%), coastal Malays (7.5%) and others (26%). Other than the data above, (a) what other data can you obtain from the population distribution in Indonesia? (b) how can this data be obtained? 1 2. Change each of the following fractions to a percentage. (a) 3 5 (b) 3 10 (c) 5 8 Thinking ©Praxis Publishing_Focus On Maths

239 Statistics CHAPTER 7 7.1 Data Data is a collection of facts, such as numbers, words, measurements, observations or just descriptions of things. A Types of data Types of data are collected and used for research purposes. They can be used to find information about the population of a town or country, or used by a business to plan advertising campaigns or used to make predictions about the future. Data can be classified as qualitative or quantitative. • Qualitative data is descriptive information (it describes something). • Quantitative data is numerical information (numbers). (I) Qualitative data Qualitative data represents some characteristics or attributes. Furthermore, they represent descriptions which we may observe that we cannot compute or calculate. For example, • Your friends’ favourite holiday destinations. • The most common given names in your town. • How people describe the smell of a new perfume. (II) Quantitative data Quantitative data can be measured and not just be observed. We can represent them numerically and even perform calculations. For example, • Height (Continuous), • Weight (Continuous), • Petals on a flower (Discrete), • Customers in a shop (Discrete). Design a questionnaire for collecting data to answer each question. Give at least 4 possible answers to your question each time. (a) What is the favourite food of Grade 7 students? (b) What is the favourite pet of the students in your school? (c) Who is the favourite athlete of the people in your province? 2 ©Praxis Publishing_Focus On Maths

240 CHAPTER 7 Statistics Quantitative data can be discrete or continuous: • Discrete data can only take certain values (like whole numbers). Discrete data is one which can take into consideration only certain specific values instead of a range of values. For instance, data which is on the blood group of a specific population or on their genders is known as discrete data. Also, bar charts are a common way to represent this data. • Continuous data can take any value (within a range). These are data that can take values between a certain range with the highest and lowest values. The difference between the highest and lowest value is called the range of data. For example, the age of persons can take values even in decimals or so is the case of the height and weights of the students of your school. These are classified as continuous data. Continuous data can be tabulated in what is called a frequency distribution. They can be graphically represented using histograms. In other words, discrete data is counted but continuous data is measured. (III) Primary data Primary data is data that has been collected from the original source for a specific purpose, for example, if a school wanted to know what their students thought of the school canteen service, they would question the pupils directly. (IV) Secondary data Secondary data is data sourced from a place that originally collected it. This means that this type of data has already been collected by some researchers or investigators in the past and is available either in published or unpublished form. For example, information available on websites or in other repositories, books, journals, etc. B Classifying Data Statistical questions are questions that can be answered by collecting data where the data are diverse or varies. Statistical question Explanation What are the marks of the students from Class 7 Dinamik in the Mathematics test? There is variability in the students’ marks. For example, 85 marks, 60 marks and so on. What are the favourite colours of the students from Class 7 Dinamik? There is diversity in the favourite colours of the students. For example, blue, red, green and other colours. After generating the statistical question, process of data collection can be carried out. (a) Counting Data are whole numbers as counting is done one at a time. (b) Measuring Data can be whole numbers, decimals or fractions as measuring instruments like rulers and thermometers are used. There are several methods of data collection. For example, interview, survey, observation and experiment. ©Praxis Publishing_Focus On Maths

241 Statistics CHAPTER 7 Form groups of 10 students. Do a survey about the number of storybooks read by each of your group members in a given month. Record the data systematically and present it to your class. team work EXAMPLE 1 State whether the following data are obtained by counting or measuring. (a) The depth of water at different locations in the Sunda Straits. (b) The number of spectators for six different football matches. Solution: (a) Measuring (b) Counting EXAMPLE 2 State the most suitable method of data collection for the following situations: (a) The favourite sports of a group of students. (b) The percentage of sugar content in a tin of 170 g of condensed milk. (c) The most popular cendol stall at a hawker complex. (d) The scores obtained by six football teams in a football league. Solution: (a) Counting by conducting a survey. (b) Measuring by conducting an experiment. (c) Counting by observation or conducting interview. (d) Counting by observation. Do you think your results would be the same if you asked the same questions in another grade 7 class? Thinking ©Praxis Publishing_Focus On Maths

242 CHAPTER 7 Statistics C Collecting and recording data Data collected are usually recorded systematically in the form of a table. Objective: Understand the concept of data. Instruction: Do this activity in a group of four. 1. Collect the following information from each student in your class. (a) The length of thumb. (b) The numbers of siblings in family. (c) The height of the student. (d) The number of pencils own by each student. 2. Classify each of the data obtained into two categories. (a) Data that obtained by counting. (b) Data that obtained by measuring. 3. Compare your results with your group members. 1 EXAMPLE 3 A college in Jakarta has the following number of students: 15 students from Nigeria, 26 students from China, 39 students from Singapore and 950 students from Indonesia. Record the data systematically. Solution: Country Number of students Nigeria 15 China 26 Singapore 39 Indonesia 950 EXAMPLE 4 Classify the following data into qualitative data or quantitative data. Give three possible examples for each given data. Hence, if the data is quantitative, determine whether the data is discrete or continuous. (a) Heights of a group of 15 years old students. (b) The ways employees come to their workplace. (c) The favourite sports of students in a class. (d) The number of students in Class 1 Bestari who wear spectacles. ©Praxis Publishing_Focus On Maths

243 Statistics CHAPTER 7 Solution: (a) Quantitative data. For example, the heights of the students can be 155.2 cm, 160 cm, 158.4 cm and so on. ➞ Continuous data (b) Qualitative data. For example, employees come to their workplace by driving a car, boarding a bus, riding a motorcycle or by some other forms of transport. (c) Qualitative data. For example, the favourite sports of the students can be football, netball, volleyball or some other sports. (d) Quantitative data. For example, the number of students who wear spectacles can be 15 people, 12 people, 9 people or any other whole number. ➞ Discrete data Practice 7.1 Basic Intermediate Advanced 1 State whether the following data are obtained through counting or measuring. (a) The height of an oak tree. (b) The number of plates of chicken rice sold by a stall. (c) The amount of time Suli spent to do her work on Tuesday. (d) The number of radio stations having their broadcasts on air on Sunday. B In August, Steve’s family spent $250 on transport, $200 on clothes, $560 on food, $180 on utility bills and $280 on entertainment. Record the data systematically. C Ram is 1.52 m tall, while the heights of Adam, Nora and Almeida are 1.56 m, 1.47 m and 1.75 m respectively. Record the data systematically. 4 State the most suitable method of data collection for the following situations. (a) Number of visitors to Surabaya Zoo in a day. (b) The most popular pop song played last week. (c) The amount of fats in 100 grams of french fries. (d) The travelling time to school of a group of students from their respective house. 5 Classify the following data into qualitative or quantitative data. Give three possible examples for each given data. If it is a quantitative data, determine whether the data is discrete or continuous. (a) Favourite fruits of students. (b) The mass of Grade 7 students. (c) The most popular brands of laptops owned by consumers. (d) The quantity of rainfall recorded in one month. (e) Marks obtained in a History test by students. (f) The genre of songs stored in a smartphone. ©Praxis Publishing_Focus On Maths

244 CHAPTER 7 Statistics 7.2 Presenting Data in Table A Determining the frequency of data From Activity 2, we can see that the number of times a piece of information appears in a collection of ungrouped data is called frequency. Ungrouped data is the raw data that have not been processed. After the process of data collection, the process of data organisation is carried out by constructing a frequency table. The frequency of an item in the data can be determined by counting or grouping the tally marks in the frequency table. To determine frequencies, we either: (a) Count – count each type of data as it appears or (b) Tally – count by grouping data in fives. The frequency table presents the data in rows and columns in a more organised manner. Objective: To explore the concept of frequency. Instruction: Do this activity in a group of four. 1. The following data shows the saving money ($) from each student in a class for a given week. 4 4 5 5 2 4 5 4 3 5 5 5 3 2 2 6 5 5 6 4 5 6 3 2 5 3 2 5 5 4 2. Record all the data above systematically. 3. Find the number of students who save $5 in the given week. 4. Discuss and present your findings of the above data to your class. 2 EXAMPLE 5 23 31 20 27 31 31 20 27 31 23 20 31 23 27 31 27 31 27 20 31 The data shows the number of training hours in a week for 20 swimmers. Determine the frequency of each number of hours by (a) counting, (b) tallying. The total frequency, obtained by adding up all the different frequency values, must be the same as the number of data collected. ©Praxis Publishing_Focus On Maths

245 Statistics CHAPTER 7 Solution: (a) The frequency for: 20 is 4 23 is 3 27 is 5 31 is 8 (b) Number of hours Tally Frequency 20 |||| 4 23 ||| 3 27 |||| 5 31 |||| ||| 8 B Constructing tally charts and frequency tables Both tally charts and frequency tables present data in an organised way in rows and columns. Data frequencies are shown as tallies in a tally chart and numbers in a frequency table. EXAMPLE 6 4 7 7 10 8 10 8 7 10 8 8 4 8 4 10 8 10 4 8 4 The data shows the number of telephone calls a family received over a period of time. From the data, construct (a) a tally chart, (b) a frequency table. Solution: (a) Number of calls Tally 4 |||| 7 ||| 8 |||| || 10 |||| (b) Number of calls Frequency 4 5 7 3 8 7 10 5 EXAMPLE 7 Red Red Blue Blue Blue Yellow Yellow Red Blue Yellow Blue Yellow Red Yellow Blue Blue Red Blue Yellow Blue Blue Blue Red Red Yellow Red Blue Red Red Blue The data above shows the favourite colours of 30 students. Organise the data by constructing a frequency table. ©Praxis Publishing_Focus On Maths

246 CHAPTER 7 Statistics Solution: Colour Tally Frequency Red |||| |||| 10 Blue |||| |||| ||| 13 Yellow |||| || 7 Total 30 EXAMPLE 8 3 2 1 2 1 2 3 3 1 4 1 1 2 4 3 1 2 1 1 2 The data above shows the daily training duration (in hours) for 20 badminton players. Organise the data by constructing a frequency table. Solution: Duration (hours) Tally Frequency 1 |||| ||| 8 2 |||| | 6 3 |||| 4 4 || 2 Total 20 EXAMPLE 9 Word Frequency She 26 Did 11 The 17 Went 5 Why 9 The frequency table shows the number of times five different words appear in a short story. State (a) the word with the highest frequency, (b) the word with the lowest frequency, (c) the word with a frequency of 17. Solution: (a) She (b) Went (c) The • Note that the total frequency is the same as the number of data collected. • Each time the frequency reaches a value of 5, the tallies are grouped and marked as ‘IIII’. The data shown is discrete data. Discrete data in the frequency table are usually arranged in an ascending order. ©Praxis Publishing_Focus On Maths

247 Statistics CHAPTER 7 C Obtaining information from frequency table EXAMPLE 10 Time (a.m.) 6.10 6.15 6.20 6.25 6.30 6.35 Frequency 6 3 12 5 7 2 The table shows the times at which a class of 35 students left their homes for school on Monday. (a) How many students left their homes at or after 6.25 a.m.? (b) What is the difference between the number of students who left their homes at 6.15 a.m. and 6.30 a.m.? (c) What is the most frequent time at which the students left for school? (d) What is the percentage of students who left their homes at or after 6.20 a.m.? Solution: (a) Number of students who left their homes at or after 6.25 a.m. = 5 + 7 + 2 = 14 (b) Difference between the number of students who left their homes at 6.15 a.m. and 6.30 a.m. = 7 – 3 = 4 (c) The most frequent time at which the students left for school was 6.20 a.m. (d) Number of students who left their homes at or after 6.20 a.m. = 12 + 5 + 7 + 2 = 26 Percentage of students who left their homes at or after 6.20 a.m. = 26 35 × 100% = 74 2 7 % EXAMPLE 11 Day Number of watermelons Sunday 49 Monday 35 Tuesday 41 Wednesday 30 Thursday 28 Friday 34 Saturday 33 The table above shows the number of watermelons sold at a stall in a week. ©Praxis Publishing_Focus On Maths

248 CHAPTER 7 Statistics (a) What is the total number of watermelons sold? (b) What is the difference between the number of watermelons sold on Sunday and Monday? (c) What is the percentage of watermelons sold on Wednesday compared to the whole week? Solution: (a) Total number of watermelons sold = 49 + 35 + 41 + 30 + 28 + 34 + 33 = 250 (b) Difference in the number of watermelons sold = 49 – 35 = 14 (c) Percentage of watermelons sold on Wednesday = 30 250 × 100% = 12% Practice 7.2 Basic Intermediate Advanced A 3 5 4 5 3 5 3 4 5 3 4 3 5 6 3 3 5 3 6 3 6 5 3 3 4 The data shows the number of magazines subscribed to in 25 households. State the frequency of each number by (a) counting, (b) tallying. B 2.50 3.00 3.50 3.00 4.00 3.00 3.00 4.00 2.50 4.00 2.50 3.50 3.00 3.50 4.00 3.00 3.00 4.00 3.00 2.50 3.00 2.50 4.00 3.00 3.50 3.00 4.00 3.00 2.50 3.50 2.50 4.00 2.50 3.50 3.00 4.00 The data shows the price, in $, of a plate of pasta from different stalls in a town. (a) Construct a frequency table by tallying. (b) What was the most frequent price? (c) How many stalls sold their pasta at $4.00? (d) Find the number of stalls which sold pasta at a price less than $3.50. C C J C A A J J C C A J C J C J A C A C J A C A J C C A C J A The data above shows the tourist destinations picked by a group of tourists in a survey. Given that A represents Australia, J represents Japan and C represents China. (a) Organise the data by constructing a frequency table. (b) State the tourist destinations that are equally popular. 4 1 3 2 1 4 1 2 1 1 1 3 1 2 4 3 1 2 1 1 3 1 1 2 1 3 1 1 2 The results of a survey on the average number of hours the employees of a company spent on the Internet daily are shown above. (a) Construct a frequency table. (b) What was the fraction of employees who spent one hour on the Internet? ©Praxis Publishing_Focus On Maths

249 Statistics CHAPTER 7 (c) What was the total number of employees who spent 2 and 3 hours on the Internet? 5 5 2 4 5 3 4 3 4 3 4 3 3 2 3 4 5 4 3 2 2 3 5 4 2 The data above shows the number of pens owned by 24 students. (a) Organise the data by constructing a frequency table. (b) Determine the number of students who owned the most number of pens. (c) What is the difference between the number of students who owned 4 pens and 2 pens? 6 Heartbeats per minute 50 55 60 65 70 75 Number of athletes 8 14 25 43 x 53 200 athletes underwent a medical examination and their resting heartbeats per minute were recorded. The results are shown above. Find (a) the value of x, (b) the ratio of the number of athletes whose heartbeat was less than 60 to the total number of athletes. 7 Day Mon. Tue. Wed. Thur. Fri. Sat. Sun. Number of families 24 39 31 28 59 205 184 The table shows the results of a survey on the day when families ate out. (a) How many families took part in this survey? (b) What was the difference in the number of families who ate out on Monday and Saturday? (c) What was the percentage of families who ate out on Saturday? 8 Number of shots which hit the target Number of athletes 20 18 21 25 22 p 23 34 24 14 25 27 150 athletes took part in a shooting practice. The results of the number of shots which hit the target are recorded in the table above. Find (a) the value of p, (b) the ratio of the number of athletes who hit the target less than 23 times to the total number of athletes who took part in the practice. 7.3 Bar Chart A Constructing bar charts to represent data Data can be represented in graphic form to attract the reader and ensure that the information conveyed is easy to understand. Bar chart, line graph and pie chart are several types of data representation for ungrouped data. The suitability of a data representation depends on the type of data collected and the purpose of the information obtained. A bar chart or bar graph represents data in the form of bars of equal width. The bars can be drawn either vertically (vertical bar chart) or horizontally (horizontal bar chart). The height or length of each bar gives the frequency of the corresponding data item. Dual bar charts are used to compare two collections of data. ©Praxis Publishing_Focus On Maths

250 CHAPTER 7 Statistics The steps to construct a bar chart: A Based on the maximum frequency of the data, choose a suitable scale for the vertical or horizontal bars. B Determine the length of each bar, based on the data frequency. C Draw a bar for each frequency and separate the bars by equal spaces. D Write the title above the bar chart. A key is needed for dual bar charts only. Maths LINK Science Meteorologists are scientists who study weather. They record weather data over days, months, and years. It is important that they display these data for others to understand. EXAMPLE 12 Day Mon. Tue. Wed. Thur. Fri. Distance d (km) 8 10 14 7 12 The frequency table shows the distances Michael ran over a period of 5 days. Construct a horizontal bar chart for the data. Solution: Mon. 0 2 84 6 Distance (km) Distance Michael ran from Monday to Friday Day 10 12 14 Tue. Wed. Thur. Fri. When fixing a scale, choose a uniform scale which is easy to plot. Horizontal bar chart is suitable for data with many categories and with long headings which could not fit well on the limited space of the axis. ©Praxis Publishing_Focus On Maths

251 Statistics CHAPTER 7 EXAMPLE 13 Shop A B C D E Number of watches 6 11 9 15 7 The frequency table above shows the number of watches sold in 5 shops in a day. Construct a bar chart to represent the given data and justify the suitability of this data representation. Solution: Draw a vertical bar chart. A B C D E 0 Number of Watches Sold Number of watches 4 8 Shop 12 16 The bar chart is suitable to compare the number of watches sold in 5 different shops. Draw a horizontal bar chart. A B C D E 0 Number of Watches Sold 4 8 Number of watches Shop 12 16 B Obtaining information from bar charts EXAMPLE 14 0 10 20 30 40 50 60 70 Month Jan. Feb. Mar. Apr.. May. Mr Jordan’s Telephone Bill from January to May Amount ($) Fixed line Mobile phone The dual bar chart shows Mr Jordan’s telephone usage for five months. Calculate (a) the total bill for his mobile phone and fixed line phone in April, ©Praxis Publishing_Focus On Maths

252 CHAPTER 7 Statistics (b) the greatest decrease in the mobile phone bill between two consecutive months, (c) the difference between the total bill for his mobile phone and fixed line phone over the five months, (d) his average fixed line phone bill for the five months. Solution: (a) Total bill in April = 25 + 70 = $95 (b) The greatest decrease is between April and May. The greatest decrease = 70 – 60 = $10 (c) Total bill for mobile phone = 50 + 45 + 40 + 70 + 60 = $265 Total bill for fixed line phone = 30 + 40 + 45 + 25 + 35 = $175 Difference = $265 – $175 = $90 (d) Average fixed line phone bill = 175 5 = $35 C Solving problem involving bar charts EXAMPLE 15 0 50 100 150 200 250 300 350 400 450 Shop A B C D E Sales Figures of Watches for Five Shops Number of watches The vertical bar chart shows the sales figures of watches for five shops in December. (a) What was the difference in the number of watches sold between the shops with the highest and the lowest sales? ©Praxis Publishing_Focus On Maths

253 Statistics CHAPTER 7 (b) If Shop E had an increase of 20% in sales in the following month, while Shop A sold 30 watches fewer, what was the total sales for the two shops? (c) If the average value of a watch was $150, calculate the total value of the watches sold by all five shops in December. Solution: (a) Difference = 450 – 175 = 275 watches (b) Shop E : 120% of 400 = 480 watches Shop A : 250 – 30 = 220 watches Total sales for the two shops = 480 + 220 = 700 watches (c) Total number of watches = 250 + 175 + 450 + 325 + 400 = 1600 watches Total value = 1600 × 150 = $240 000 Shop C had the highest sales and Shop B the lowest. The bar chart shows the profits of Company X over a period of four years. Based on the bar chart, answer the following questions. (a) Is the change in the height of bars from year 2019 to year 2020 the same as that from year 2021 to year 2022? (b) Is the difference in profits from year 2019 to year 2020 the same as that from year 2021 to year 2022? (c) In your opinion, does the bar chart display the data accurately? Profits of Company X 0 5 10 12 14 Year Profit ($ million) 2019 2020 2021 2022 ©Praxis Publishing_Focus On Maths

254 CHAPTER 7 Statistics Practice 7.3 Basic Intermediate Advanced 1 Day Friday Saturday Sunday Number of pendrives 100 150 225 The table shows the number of pendrives sold by a booth at a PC Fair in three days. On a square grid with sides of 1 unit, construct a bar chart to show the data. Use a scale of 2 units to 50 pendrives on the vertical axis. B Grade A B C D E Number of students 7 3 12 6 11 The table shows the grades achieved by a class of students in a test. Based on the data, construct a vertical bar chart. C Dini’s Annual Income 0 0.8 1.6 2.4 3.2 4.0 4.8 0.4 1.2 2.0 2.8 3.6 4.4 Year Income ($ ten thousands) 2018 2019 2020 2021 2022 The bar chart above shows Dini’s annual income over a period of 5 years. Convert the representation to another suitable representation and justify your choice. 4 The bar chart shows the number of mobile phones sold by a shop over a period of five months. What is the greatest increase between two consecutive months? 0 10 20 30 40 Jan. Feb. Mar. Apr. May Month Number of mobile phones Number of Mobile Phones Sold by a Shop 5 The bar chart shows the number of rainy and sunny days in a town for three consecutive months. What fraction of the total number of days were rainy days? 0 2 4 6 8 10 12 14 16 18 20 Number of days Weather of a Town for Three Months Sunny Jan. Feb. Month Mar. Rainy ©Praxis Publishing_Focus On Maths

255 Statistics CHAPTER 7 6 The incomplete bar chart shows the number of boxes of chocolates sold by a shop in one week. The total number of boxes of chocolates sold for the four different flavours was 500. The ratio of the number of boxes of coffee-flavoured chocolates sold to the number of boxes of plain chocolates sold was 3 : 2. Complete the bar chart. 0 40 80 120 160 Vanilla Coffee Strawberry Plain Number of boxes Flavour Number of Boxes of Chocolates Sold by a Shop in a Week 7 0 10 20 30 40 50 60 70 Value ($) Sales of Ice Cream for Six Days Day 80 90 100 110 120 130 Mon. Tue. Wed. Thur. Fri. Sat. The horizontal bar chart shows the sales of an ice cream vendor for six days. (a) On which day did he sell the most ice cream? (b) How much more did he sell on Wednesday compared to Monday? (c) Calculate his total sales for the six days. (d) If the vendor made a profit of 15% from the sales of ice cream, calculate his profit on Thursday. H The bar chart shows the number of people who went to a particular beach from January to April. What was the total number of children? 0 2 4 6 8 10 12 14 16 18 20 22 Month Number of People at a Beach Adults Jan. Feb. Mar. Apr. Number of people (thousands) Children 9 These graphs display the same data. Which graph is misleading? Why? Graph A Food Drive Results 0 50 100 150 200 Person Cans Collected Meg Russ Vic Graph B Food Drive Results 100 125 150 175 200 Person Cans Collected Meg Russ Vic ©Praxis Publishing_Focus On Maths

256 CHAPTER 7 Statistics 7.4 Line Graph A Representing data using line graphs A line graph shows data that have been collected over a time period. The frequency values are plotted vertically and the time values are plotted on the horizontal axis. Line graph is a type of data representation that uses straight lines to join the points representing the values of the data. Line graph is suitable to display the changes in data over a period of time. The steps to construct a line graph: A Based on the maximum frequency of the data, choose a suitable scale. B Draw the horizontal axis and the vertical axis, and plot the data points. C Join the points using straight lines. The table and graph show how Haye’s height changed as she got older. Age (years) Height (cm) Age (years) Height (cm) 2 83 11 142 3 95 12 151 4 101 13 158 5 109 14 160 6 116 15 161 7 120 16 162 8 128 17 162 9 135 18 162 10 139 19 162 For the graph: (a) What is the title of the graph? (b) What does each axis show? (c) Why are the points are joined? Are the data discrete or continous? (d) What conclusions can you make from the graph? 3 Haye’s Growth in Height 0 40 80 120 160 Age (years) Height (cm) 2 4 6 8 10 12 14 16 18 20 ©Praxis Publishing_Focus On Maths

257 Statistics CHAPTER 7 EXAMPLE 16 Time (a.m.) Temperature (°C) 9.00 30 9.05 44 9.10 60 9.15 80 9.20 90 9.25 110 The table shows the temperature of a pot of curry as it is being cooked. Construct a line graph for the data. Solution: 0 9.00 9.05 9.10 Time (a.m.) 9.15 9.20 9.25 20 40 60 80 100 120 Temperature of a Pot of Curry Temperature (°C) EXAMPLE 17 Month Aug. Sep. Oct. Nov. Dec. Quantity of rainfall (cm) 18 23 27 32 54 The table shows the quantity of rainfall recorded in Jakarta from the month of August until December 2021. Construct a line graph to represent the given data and justify the suitability of this data representation. Line graphs are suitable to show the changes in data over a period of time such as temperature change at a region or the height or mass change of a person. ©Praxis Publishing_Focus On Maths

258 CHAPTER 7 Statistics Solution: Quantity of Rainfall in Jakarta Quantity of rainfall (cm) 0 10 20 30 40 50 60 Aug. Sept. Oct. Nov. Dec. Month The line graph is suitable to show the change in the quantity of rainfall in Jakarta over the last 5 months in the year 2021. B Obtaining information from line graphs EXAMPLE 18 60 Jan. Feb. Mar. Mark Month Dahlia’s Science Test Marks Apr. May Jun. 65 70 75 80 85 90 The line graph shows the marks obtained by Dahlia for her science tests. (a) In which month did she have the highest score? (b) State the months in which she obtained 85 or more marks. (c) Between which two months was there the greatest increase in marks? Solution: (a) April (b) The months were February, April and June. (c) The greatest increase in marks was between May and June. ©Praxis Publishing_Focus On Maths

259 Statistics CHAPTER 7 C Solving problems involving line graphs EXAMPLE 19 45 2016 46 47 48 49 50 51 52 53 54 55 56 57 58 59 2017 2018 Time (s) Year Magesh’s Best 400 m Times 2019 2020 2021 The line graph shows Magesh’s best times for the 400 m track event over a period of 6 years. (a) From which year onwards did he run under 55 seconds? (b) What was his improvement in time after 6 years of training? (c) What was his improvement percentage in time from 2019 to 2021? Solution: (a) From 2018 onwards. (b) Improvement = Slowest time – Fastest time = 57.5 s – 49 s = 8.5 seconds (c) Difference in time = 52 s – 49 s = 3 seconds Improvement percentage in time = 3 52 × 100% = 5.77% ©Praxis Publishing_Focus On Maths

260 CHAPTER 7 Statistics EXAMPLE 20 Mass of Hamzah 0 50 60 70 80 2018 2019 2020 Year Mass (kg) 2021 2022 The line graph shows the changes in Hamzah’s body mass from the year 2018 to the year 2022 in a healthy lifestyle programme. (a) State the total reduction of Hamzah’s mass from the year 2018 to the year 2022. (b) State two consecutive years when Hamzah’s mass recorded the highest reduction. (c) Predict Hamzah’s mass in the year 2023 if he continues with the programme. Solution: (a) Total reduction of mass = 73 – 54 = 19 kg (b) Between the year 2020 and 2021. The drop in the graph is most noticeable. (c) The line graph shows a decreasing trend from year 2018 to year 2022, in which Hamzah’s mass decreased by 4 kg, 3 kg, 8 kg and 4 kg over the period. If Hamzah continues with the programme, his mass will be 51 kg in the year 2023. EXAMPLE 21 Coronavirus disease (COVID-19) is a world infectious disease caused by the SARS-CoV-2 virus. This virus has infected to most of the people in the world. From January 2022 to September 2022, there were more than 100 000 new cases of Covid-19 in Indonesia. The line graph shows the monthly number of Covid-19 cases in Indonesia from January 2022 to September 2022. ©Praxis Publishing_Focus On Maths

261 Statistics CHAPTER 7 Covid-19 Monthly Cases 0 25 000 50 000 75 000 Month Number of cases Jan 2914 55 377 30 154 3437 413 1168 3241 3177 1747 Feb Mar Apr May Jun Jul Aug Sep (a) In which month are there the highest number of cases? (b) State the three months that recorded the highest reduction in monthly new cases. (c) Predict the number of cases in early year 2023 if the reduction trend of new cases of Covid-19 continues. Solution: (a) February. (b) March, April and May. (c) The line graph shows a decreasing trend from August 2022 until September 2022. If this trend continues, there will be lesser cases in the following months and in early year 2023. Practice 7.4 Basic Intermediate Advanced A The line graph shows the number of employees in NewTech Company from 2014 to 2019. (a) How many employees were there in 2014? (b) Which two consecutive years had the greatest increase in the number of employees between those two years? (c) How many more employees were there in 2019 compared to 2016? 0 50 100 150 200 250 300 350 400 Year 2014 2015 2016 2017 2018 2019 Number of employees Number of Employees in NewTech Company from 2014 to 2019 ©Praxis Publishing_Focus On Maths

262 CHAPTER 7 Statistics B Selling Price of Model Y Car Selling price ($ thousand) Year 20 22 24 26 28 30 32 34 36 38 40 0 2010 2012 2014 2016 2018 2020 The line graph above shows the selling price of model Y car that is recorded every two years starting from the year 2010. (a) What is the price of the car in the year 2014? (b) What is the increase in price of the car over the period of 10 years? (c) Calculate the percentage of increase in the price of the car in the year 2018 compared to the year 2014. (d) A car manufacturer will obtain $8000 for every unit of car sold in the year 2020. If the total amount of car sales obtained in that year is $570 million, calculate the total amount of money obtained by the manufacturer. C The line graph shows the sales price of the car model Zippy over a period of 20 years, from 2000 to 2020. (a) How much did the car cost in 2005? (b) What was the increase in price between 2000 and 2020? (c) Calculate the percentage increase in price between 2015 and 2020. (d) The manufacturer made a profit of $8000 for each car sold in 2020. If the total sales revenue for that year was $4.75 billion, calculate the profit of the manufacturer. 0 10 20 30 40 50 60 70 80 90 100 Year 2000 2005 2010 2015 2020 Sales Price of Model Zippy Car from 2000 to 2020 Sales price ($ '000) D For the following data representation, state whether the data is displayed accurately. Suggest a way to represent the data ethically. Changes in Temperature of a Liquid Over Time 32 0 8 4 Time (minutes) 48 4 16 2 86 Temperature (°C) 7.5 Pie Chart A Constructing pie charts to represent data A pie chart is a statistical representation by which areas of sectors of a circle are used to represent the data quantities. For example, the diagram is a pie chart displaying the students in each grade in a school. To construct a pie chart, the circle is divided into different sectors based on the quantity. 80° Grade 1 68° Grade5 Number of Students in a School 61° Grade 4 77° Grade 3 74° Grade 2 ©Praxis Publishing_Focus On Maths

263 Statistics CHAPTER 7 For example, each sector in the pie chart above corresponds to the number of students in each grade. The angle of each sector is proportional to the number of students represented in each sector. In constructing a pie chart, the following steps are applied: 1 Calculate the angle of each sector. Angle of sector = Quantity Total × 360° or Angle of sector = Percentage 100 × 360° 2 Draw a circle and divide the circle into sectors corresponding to the angles calculated. 3 Label the pie chart with a suitable title and appropriate label for each group of data. EXAMPLE 22 Race Indonesian Chinese Indian Others Number of students 21 16 2 1 The table shows the racial distribution of students in Grade 7A. Using a pie chart, illustrate the racial distribution of students in the class. Solution: Race Number of students Angle of sector Indonesian 21 21 40 × 360° = 189° Chinese 16 16 40 × 360° = 144° Indian 2 2 40 × 360° = 18° Others 1 1 40 × 360° = 9° Total 40 360° EXAMPLE 23 The table shows the different colours of the new Aspira car bookings placed by a group of customers. Construct a pie chart to represent the data and justify the suitability of this data representation. Pie chart is not suitable for data consisting of many categories because the sizes of the sectors will become smaller and too close to each other until the values of the angles become less accurate. Pie chart is more suitable for comparing data not more than 7 categories. Colour Number of cars Yellow 18 Red 10 White 5 Blue 7 Indonesian 189° 18° Indian 9° Others Chinese 144° Racial Distribution of Students in Grade 7A ©Praxis Publishing_Focus On Maths

264 CHAPTER 7 Statistics Solution: Colour Number of cars Fraction of circle Angle of sector Yellow 18 18 40 18 40 × 360° = 162° Red 10 10 40 10 40 × 360° = 90° White 5 5 40 5 40 × 360° = 45° Blue 7 7 40 7 40 × 360° = 63° Total 40 1 360° The pie chart is suitable to compare the different colours of the Aspira car bookings placed by the customers. Colours of Aspira Car Bookings Red Blue White 162° 63° 45° Yellow B Obtaining and interpreting information from pie charts Pie charts are used to display data when the proportions of a whole are more important than the numerical values. We can interpret information and draw some conclusions from a pie chart. EXAMPLE 24 All the Grade 7 students took part in a survey on their favourite hot drinks. The results were shown in the pie chart. (a) Which drink was the least preferred by the Grade 7 students? (b) Which was the most popular drink among the Grade 7 students? (c) How many per cent of the students liked hot chocolate? Solution: (a) Milk was the least preferred drink by the Grade 7 students. (b) Tea was the most popular drink among the students. Tea Coffee Chocolate Milk Favourite Hot Drinks of Grade 7 Students The smallest sector is milk. The largest sector is tea. ©Praxis Publishing_Focus On Maths

265 Statistics CHAPTER 7 (c) Percentage of students who liked hot chocolate = 90° 360° × 100% = 25% EXAMPLE 25 The pie chart shows the results of a survey conducted regarding the favourite food of a group of students. (a) Which type of food is the least favourite of the students? Explain. (b) What is the percentage of students who like chicken rice? Solution: (a) Angle of sector for curry noodles = 360° – 125° – 90° – 80° = 65° Curry noodles is the least favourite of the students because the angle of sector is the smallest. (b) Percentage of students who like chicken rice = 90° 360° × 100% = 25% Curry noodles Fried noodles Fried rice Chicken rice 125° 80° Favourite Food of Students C Solving problems involving pie charts EXAMPLE 26 The pie chart shows the sales of books in a bookshop in a certain week. Given that the number of comics sold was 50. (a) What was the total sales? (b) How many novels were sold? (c) Find the percentage of each type of book sold. Solution: (a) Number of comics sold = 50 Angle of sector for comics = 120° 50 Total sales × 360° = 120° Total sales = 50 × 360° 120º = 150 Storybooks Novels Comics 120° 204° Sales of Books ©Praxis Publishing_Focus On Maths

266 CHAPTER 7 Statistics (b) Angle of sector for novels = 360° – 204° – 120° = 36° Number of novels sold = 36° 360° × 150 = 15 (c) Percentage of storybooks sold = 204° 360° × 100% = 56.67% Percentage of comics sold = 50 150 × 100% = 33.33% Percentage of novels sold = 100 – (56.67 + 33.33) = 10% EXAMPLE 27 The pie chart shows the hobbies of 144 students. Calculate the difference between the number of students who like jogging and the number of students who like swimming. Solution: Stage 1: Understand the problem List the facts and the question. Facts: Hobbies for 144 srudents. 165º is for jogging. 90º is for cycling. 45º is for camping. Unknown for swimming. Question: Find the difference between the number of students who likes jogging and number of students who like swimming. Stage 2: Think of a plan • One whole turn is 360º. • Find the angle sector for swimming. • Find the number of students for jogging and swimming. • Then, find the difference for jogging and swimming. 165° 45° Jogging Cycling Swimming Hobbies of 144 students Camping ©Praxis Publishing_Focus On Maths

267 Statistics CHAPTER 7 Stage 3: Carry out the plan Number of students who like jogging = 165° 360° × 144 = 66 Angle of sector for swimming = 360° – 165° – 90° – 45° = 60° Number of students who like swimming = 60° 360° × 144 = 24 Difference= 66 – 24 = 42 students Stage 4: Look back Difference = 1 165° 360° × 144 2 – 1 360º – (165° + 90º + 45º) 360° × 144 2 = 42 students When you see a set of data, how do you decide the best way to display the data? Use the examples from this lesson in your answer. Critical Thinking Three students surveyed the Grade 7 students in their school. They asked: "How many times did you use a vending machine last week: 0 times, 1 – 5 times, 6 – 10 times, or more than 10 times?" Amrin displayed the results on a pie chart. Frendi used a bar graph. Stephen used tally chart and frequency table. Grade 7 Students’s Vending Machine Survey 6 – 10 times, 13% More than 10 times, 11% 1 – 5 times, 41% 0 times, 35% Grade 7 Students’ Vending Machine Survey 0 8 4 16 20 24 12 Number of Times Number of Students 0 1-5 6-10 More than 10 4 ©Praxis Publishing_Focus On Maths

268 CHAPTER 7 Statistics Number of times Tally Frequency 0 |||| |||| |||| |||| 19 1 – 5 |||| |||| |||| |||| ||| 23 6 – 10 |||| || 7 More than 10 |||| | 6 (a) What are the strengths and limitations of each graph or table? (b) Which type of presentation is appropriate? Justify your answer. Practice 7.5 Basic Intermediate Advanced A The types of hot beverages sold by a cafe are coffee (45%), tea (35%), chocolate (15%) and others (5%). Show these data using a pie chart and label it clearly. B Flavour Chocolate Coffee Strawberry Vanilla Others Number of people 34 29 24 19 14 The table shows the favourite flavours of ice cream of 120 people. Illustrate the information above using a pie chart. C Food Others Rent 126° Monthly Expenditure of a Family (a) Which category took up the highest amount of the family expenditure? (b) What fraction of the monthly expenditure was spent on rent? (c) How much was the total monthly expenditure if $9800 was spent on food? D Others Ayla Livina 167° Cars Sold by a Dealer in a Certain Month Avanza 17° Given that the Ayla cars took up 1 3 of the total car sales and the Livina’s sales was $2 100 000. (a) Find the angle of the sector for (i) Ayla cars, (ii) Livina cars. (b) How much was the total car sales in that month? (c) How much was the sales of Avanza cars in that month? E USA ASEAN $98.54 billion $41.8 billion $68.81 billion Japan European Union Others 18% West Asia 2% China Hong Kong 6% 45° Country Q’s Export Destinations in a Certain Year It is given that the total of Country Q’s exports was $382.3 billion. (a) How many per cent of Country Q ’s exports was absorbed by ASEAN? ©Praxis Publishing_Focus On Maths

269 Statistics CHAPTER 7 (b) Find the angle of the sector for USA. (c) How much of the Country Q’s exports was taken in by the European Union? (d) How many per cent of Country Q’s exports was to China? (e) What fraction of Country Q ’s exports was absorbed by Hong Kong? 6 The pie chart shows Razali’s monthly expenses in college. (a) Which of the expenses is the highest? (b) State the percentage of Razali’s expenses on rent in a month. (c) What is Razali’s total monthly expenses if he spends $600 on food? Summary Summary Summary Pie chart A pie chart is a statistical representation by which areas of sectors of a circle are used to represent the data quantities. Yellow Number of Gold Medals Won by Four Teams Red 25 76° Green 19 92° Blue Data • Data is a collection of information or facts. • Data is collected by counting or measuring. Frequency The frequency of a piece of information is the number of times it occurs. Frequency table A frequency table is used to show the frequency of data. Bar chart A bar chart represents data in the form of vertical or horizontal bars of equal width. • Vertical bar chart • Horizontal bar chart • Dual bar chart 0 40 80 20 60 100 Thur. Day Number of visitors Number of Visitors to a Museum Fri. Sat. Sun. 0 20 40 6080100 Thur. Day Number of visitors Number of Visitors to a Museum Fri. Sat. Sun. 60 50 40 30 20 10 0 Thur. Day Male Number of visitors Number of Visitors to a Museum Fri. Sat. Sun. Female Line graph A line graph shows data that have been collated over a time period. Example: 0 10 20 30 April May Month Number of printers Number of Printers Sold by a Company JuneJuly Statistics Rent Fees 45° Others 108° 81° Food Razali’s Monthly Expenses ©Praxis Publishing_Focus On Maths

270 CHAPTER 7 Statistics 7 Section A Questions 1 to 3 are based on the following table. Month Number of magazines January 15 February 41 March 14 April 25 May 23 June 82 The table shows the number of magazines sold by a bookshop over a six-month period. 1. What was the total number of magazines sold in February and June? A 118 C 123 B 121 D 125 2. What was the fraction of the number of magazines sold in April out of the total number of magazines sold? A 1 8 C 1 6 B 1 7 D 1 5 3. In which month was the least number of magazines sold? A January B February C March D June 4. The table below shows the price, in $, for a plate of fried rice from several stalls in an area. Price ($) 2.50 3.00 3.50 4.00 Frequency 6 12 8 10 Determine the number of stalls that sell fried rice at a price of more than $3.00. A 6 C 12 B 18 D 30 5. 0 10 20 30 Badminton Game Number of students Favourite Games of Students Football Volleyball Basketball The bar chart shows the favourite games of 80 students. The ratio of the number of students who like to play badminton to the number of students who like to play volleyball is A 1 : 5 C 2 : 5 B 2 : 3 D 3 : 2 6. The data shows the number of visits to the cinemas within a month by a group of children. 2 1 2 1 0 3 0 3 1 1 2 2 The data above is best represented by a A Line graph C Bar chart B Frequency table D Pie chart 7. The bar chart shows the number of handphones sold at a shop in 5 days. What is the greatest difference in the sales, in $, for that period? Sale ($ hundred) 0 20 40 60 80 100 Sales of Handphones Friday Thursday Wednesday Tuesday Monday Day ©Praxis Publishing_Focus On Maths

271 Statistics CHAPTER 7 A 5000 C 50 B 4500 D 45 8. 0 10 20 30 40 50 60 2017 2018 2019 Number of Air Conditioners Sold by an Electrical Shop Number of air conditioners Year 2020 Cool Master Heat Buster The line graph shows the sales of two brands of air conditioners of an electrical shop in four consecutive years. In which year was the greatest difference between the number of air conditioners sold for the two brands? A 2017 B 2018 C 2019 D 2020 9. 120° Classical Pop 30° Country R & B Favourite Music Genres of Students The diagram shows a pie chart representing the favourite music genres of 324 students. Calculate the difference between the number of students whose favourite music genre is pop and the number of students whose favourite music genre is R & B. A 27 B 30 C 54 D 81 10. Book Number of books Fiction 26 Non-fiction 38 Reference 34 Activity books 22 Fiction Reference Activity books Non-fiction x The table shows the number of books sold by a bookshop in a month. All the information in the table is represented in the pie chart above. Calculate the value of x. A 76° C 102° B 98° D 114° Section B 1. 3 1 2 2 5 2 1 3 1 2 5 2 4 2 1 2 2 4 3 1 The data shows the number of books borrowed by 20 students in a month. (a) Construct a frequency table for the data. (b) Find the number of students who borrowed more than 3 books in a month. 2. Day Mon. Tue. Wed. Thu. Fri. Number of prepaid cards 44 x 39 32 40 The table shows the number of prepaid cards sold by a mobile phone dealer over a period of five days. Given that the total number of prepaid cards sold was 200, find the value of x. ©Praxis Publishing_Focus On Maths

272 CHAPTER 7 Statistics 3. Charity Amount ($) A 14 000 B 12 000 C 8000 D 18 000 The table shows the amount of money raised by four charities in aid of cancer patients. The information for Charity A is shown in the bar chart. Complete the bar chart to represent all the information in the table. A B C D Charity Amount of money ($ thousands) Money Raised by Charity 4. 1.0 Production of a Glove Manufacturer 2015 2016 2017 2018 2019 2020 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Year Number of gloves (billion) The line graph shows the production of a glove manufacturer from 2015 to 2020. (a) Between which two years was there a decrease in production of 200 million gloves? (b) What was the percentage increase in production between 2015 and 2020? 5. Month March April May June July Number of digital cameras 16 10 16 20 18 The table shows the number of digital cameras sold in a shop over five months. Represent all the data by drawing a line graph. Use the scale 2 cm to 4 digital cameras on the vertical axis. Month Number of Digital Camera Sold March April May June July Number of digital cameras 6. 0 100 200 300 400 500 600 700 Day Mon. Tue. Wed. Thur. Fri. Sales value ($) Sales Value of Clothes in a Boutique The line graph shows the sales value of clothes in a boutique in five days. Calculate ©Praxis Publishing_Focus On Maths

273 Statistics CHAPTER 7 (a) the difference between the highest and the lowest sales values, (b) the percentage increase in sales value for Tuesday compared to Monday, 7. x x Motorcycle Bicycle Walk 30 Modes of Transport to School Bus 50 The pie chart shows the modes of transport to school of 120 students. Find (a) the value of x, (b) the angle of the sector representing the number of students who walk to school, (c) the frequency of the mode. 8. 25% M 15% S L 40% XL Sizes of Shoes Sold The pie chart above shows the percentages of 200 pairs of shoes of different sizes sold at a shop in a week. Based on the pie chart, complete the following statements. (a) The percentage of size-L shoes sold is . (b) The number of size-L shoes sold is (c) The average sales value of clothes for the five days is . 9. Club Number of members Angle of sector Photography 18 90° Consumer 21 Arts 24 Chess 9 45° The table above shows the number of members of a few clubs in a school. The information regarding the number of members of the Photography Club is represented in the pie chart as shown in the following diagram. Complete the table and the pie chart given. Photography Number of Members According to Club ©Praxis Publishing_Focus On Maths

NOTES 274 ©Praxis Publishing_Focus On Maths

JBRB221241 ISBN 9789811729300 FOCUS-ON TEXTBOOK MATHS 7 FOCUS-ON MATHS is a complete mathematics programme specially written in line with the latest Indonesian Mathematics syllabus (Phase D) for Grade 7 to Grade 9 students. The topic coverage in each grade is arranged to address all the learning achievements (Capaian Pembelajaran) as prescribed by the Indonesian Ministry of Education. The series adopts the Singapore Maths method which is a world-class maths teaching approach. This comprehensive series builds on the foundations laid in primary mathematics and prepares learners for embarking on higher-level mathematics. With 21st Century Skills and Higher Order Thinking Skills infused in the contents; this series challenges students with engaging problem-solving tasks in real-word contexts, enabling them to become independent maths learners and build foundations for future success. Focus-on Maths comprises: • Textbook • Workbook • Teacher’s Guide • Teaching Aids ©Praxis Publishing_Focus On Maths