nota Descriptive Stat

BPL.KKM.PK (T) 08.1A/17 (a)

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BPL.KKM.PK (T) 08.1A/17 (a)

BIL HASIL KONTEN CATATAN
PEMBELAJARAN

1 LO1 Descriptive approach / Descriptive statistic

Explain the Are used to describe the basic features of the data in a study.
frequency and They provide simple summaries about the sample and the
tendencies, measures. Together with simple graphics analysis, they form
measure of central the basis of virtually every quantitative analysis of data.
tendencies &

measure of Descriptive statistics are typically distinguished from inferential
dispersion statistics. With descriptive statistics you are simply describing

what is or what the data shows.

 Descriptive Statistics are used to present quantitative
descriptions in a manageable form. In a research study
we may have lots of measures.

 Or we may measure a large number of people on any
measure. Descriptive statistics help us to simplify large
amounts of data in a sensible way. Each descriptive
statistic reduces lots of data into a simpler summary.

Frequency and percentage
 Frequency distribution – is a systematic
arrangement of numeric values from the lowest to
the highest, together with a count (or percentage)
 A percentage frequency distribution - display of data
that specifies the percentage of observations that
exist for each data point or grouping of data points.
 It is a particularly useful method of expressing the
relative frequency of survey responses and other
data.
 A frequency distribution of data can be
represented in the form of frequency tables,
histograms or bar charts.

The process of creating a percentage frequency
distribution involves :

1. first identifying the total number of observations to
be represented

2. then counting the total number of observations
within each data point or grouping of data points

3. dividing the number of observations within each
data point or grouping of data points by the total
number of observations

4. The sum of all the percentages corresponding to
each data.

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BPL.KKM.PK (T) 08.1A/17 (a)

Tables

Tables

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Tables
Histogram
Table

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Bar chart

Measures of central tendencies
a.k.a average is a single value that attempts to desribe
a set data by identifying the central position within that
set of data.

o Mean
o Mode
o Median

i) MEAN
The Mean or average is probably the most commonly
used method of describing central tendency.

To compute the mean is add up all the values and divide
by the number of values.

FORMULA FOR MEAN:
Raw Data: 15, 20, 21, 20, 36, 15, 25, 15

Mean =15+20+21+20+36+15+25+15 =20.875
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ii. MEDIAN
The Median is the score found at the exact middle of the
set of values.

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One way to compute the median is to list all scores in
numerical order, and then locate the score in the center
of the sample.
If we order the 8 scores shown above, we would get:

15,15,15,20,20,21,25,36
There are 8 scores and score #4 and #5 represent the
halfway point. Since both of these scores are 20, the
median is 20.
If the two middle scores had different values, you would
have to interpolate to determine the median.
iii) MODE
The mode is value that occurs most often or frequent.
In our example, the value 15 occurs three times.

15,15,15,20,20,21,25,36

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Measures of dispersion
o Standard Deviation
o Inter Quartile Range
o Range

Measures of dispersion
 the spread of the data value in our distribution.
 the more similar the score are to each other, the
lower the measure dispersion
 the less similar the scores are to each other, the
higher the measure of dispersion.
 In general, the more spread out a distribution,
the largest the measure of dispersion will be -
symmetrical or skewed.

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Measures of dispersion:
i. Range
ii. Inter Quartile Range (IQR)
iii. Standard Deviation

Range
 The range is difference between maximum and
minimum data values
 Example distribution, the high value is 36 and the
low is 15, so the range is 36 - 15 = 21.

Interquartile Range (IQR)
Distance between third quartile (Q3) and first quartile

Standard deviation
 The square root of the variance
 Variance – The deviation of all values from the
mean.

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BPL.KKM.PK (T) 08.1A/17 (a)

2 LO2 Normal distribution:

Explain normal - characteristics of normal distribution

distribution curve. - types of normality tests

o Histogram

o Boxplot

o Skewness & Kurtosis

CHARACTERISTICS OF NORMAL DISTRIBUTION

Characteristics:
1. Bell shape
2. Bilateral symmetry
3. Tails never touch x-axis
4. Area under curve totals 1.00
5. The mean, median, and mode are equal
6. The curve is unimodal

1.Bell shape
 Bell shape when the x –axis is scaled properly
 The tails of the distribution approach the x-axis
but never touch
 It is a bell –shaped curve, because of its
characteristics roundness at the top and
inflections on each side

2.Bilateral symmetry
 That is, the normal curve has a bilateral

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symmetry.
 In other words the left and right values to the
middle central point are mirror images.
 It implies that the size, shape and slope of the
curve on one side of the curve is identical to that
of the other.
3.Tails never touch x-axis
 The tails of the curve are asymtotic to the
baseline.
 It means that the tails of the curve approach the
baseline but never touch it.
4.Area under curve totals 1.00
The total area under the curve is equal to one.

5. The mean, median, and mode are equal
 The mean, median and mode of the normal
distribution are the same and they lie at the
centre. They are represented by 0 (zero) along
the base line. [Mean = Median = Mode]

6. The curve is unimodal
Since there is only one point in the curve which has
maximum frequency, the normal probability curve is
unimodal, i.e. it has only one mode.

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Normality test
Assumption of normality means that you should make
sure your data roughly fits a bell curve shape before
running certain statistical tests or regression.
 The concept of normality is central to statistics.
 For data to be normal, they must have the form of a

bell shape.
Types of normality tests

1. Using a graph
o Histogram
o Boxplot
o Skewness & Kurtosis

2. Statistical test
o Kolmogorov-Smirnov Goodness of Fit Test
o Shapiro-Wilk Test

Histogram
 Shape approximates as a bell -shape it suggests
that the data may have come for a normal
population.
 Using 5 characteristics

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Boxplot
 Draw a boxplot of your data. If your data comes
from a normal distribution, the box will be
symmetrical with the mean and median in the
center.
 If the data meets the assumption of normality,
there should also be few outliers.

Skewness & Kurtosis

 Skew – tilt or lack of it in a distribution.
 Right skew – the tail points to the right.
 Left skew – the tail is points left.
 A common rule of thumb test for normality – to run

descriptive statistics to get skewness and kurtosis
– divide these by the standard errors.
 Skew should be within +2 to -2 range hen the data
are normally distributed.
 Some authors use +1- to -1 as a more stringent
criterion when normality is critical
(

Kolmogorov-Smirnov Goodness of Fit Test
 This compares your data with a known distribution

(i.e. a normal distribution).
 Large sample size >50
 p value > than 0.05 normality can be assumed
 Meaning data can be assumed to be distributed

normal

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Shapiro-Wilk Test
 This test will tell you if a random sample came from

a normal distribution.
 Sample size < than 50
 p value > than 0.05 normality can be assumed
 Meaning data can be assumed to be distributed

normal

3 LO3 Data presentation

Utilised graphs, - Table

charts, and tables - Graph
in presenting data. - Chart

a.Graphs - visual display of data used to present
frequency distributions so that the shape of the

distribution can easily be seen.

b. Table / Contingency tables
Is a means displaying the relationship between two (2)

sets of nominal data.

In statistics, a contingency table (also known as a

cross tabulation or crosstab) is a type of table in a
matrix format that displays the (multivariate) frequency

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distribution of the variables. They are heavily used in
survey research, business intelligence, engineering and
scientific research

c. Chart
A chart, also called a graph, is a graphical
representation of data, in which "the data is represented
by symbols, such as bars in a bar chart, lines in a
line chart, or slices in a pie chart". A chart can
represent tabular numeric data, functions or some kinds
of qualitative structure and provides different info.

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