0 LECTURER’S NAME : PUAN HAZWANI BINTI BACHOK PREPARED BY : 1. MOHAMMAD ZAKWAN BIN ISMAIL 33DEI22F10212. DANISH HAKIMI BIN MOHD RAFI 33DEI22F10083. MOHAMAD AIDIE YUSRI BIN YUSSOF 33DEI22F10024. MUHAMMAD AFIQ BIN FAIZAL NAZRI 33DEI22F1054ELECTRICAL ENGINEERINGMATHEMATICS(DBM30043) CASESTUDYSET3
1 CONTENTS 1. Question 2. Introduction 3. Data 4. Frequency Distribution Table 5. Measure of central tendency and dispersion by using formula 5.1. Mean & Median 5.2. Mode 5.3. Mean Deviation, Variance and Standard Deviation 5.4. 1 st Quartile, 3 rd Quartile and Interquartile Range 5.5. 6 th Decile and 32 nd Percentile 6. Measure of Central Tendency by using Histogram graph 6.1. Mode from Histogram 7. Measure Quartile,Decile and Percentile by using ogive graph 7.1. Median 7.2. 1 st Quartile and 3 rd Quartile 7.3. 6 th Decile and 32 nd Percentile 8. Conclusion 9. references 23-567-910-141516-181920
2 QUESTION
3 INTRODUCTIONAn oil refinery is an industrial plant that transforms, or refinescrude oil into various usablepetroleum products suchasdiesel, gasoline, and heatingoils like kerosene. Non energy is thetotal consumption of fossil fuelsasfeedback in the chemical industry, refinery and coke even product consumed in various economicsectors, as well as the useof solidcarbon for the productionof metals and inorganic chemicals
4 STATISTICSDESCRIPTIONSTATICTICSStatistics is a branch of appliedmathematics that involvesthecollection, description, analysis, andinference of conclusions fromquantitative data. The mathematical theories behind statistics rely heavilyon differential and integral calculus, linear algebra, and probability theory. Descriptive statistics mostly focusonthe central tendency, variability, anddistribution of sample data. Central tendency means the estimateof thecharacteristics, a typical element of asample or population. It includesdescriptive statistics such as mean, median, and mode.Variability referstoaset of statistics that showhowmuchdifference there is among theelementsof a sample or population alongthecharacteristics measured. It includesmetrics such as range, variance, andstandard deviation. .There are two kinds of statistics, whichare descriptive statistics and inferential statistics.
5 INFERENTIAL STATISTICSInferential statistics are toolsthatstatisticians use to drawconclusionsabout the characteristics of apopulation,drawn from the characteristicsof asample, and to determine howcertainthey can be of the reliabilityof thoseconclusions. Based on the samplesizeand distribution, statisticianscancalculate the probability that statistics,which measure the central tendency,variability, distribution, and relationshipsbetween characteristics withinadatasample, provide an accuratepictureofthe corresponding parametersof thewhole population fromwhichthesampleis drawn. Inferential statistics are usedtomakegeneralizations about large groups, suchas estimating average demandforaproduct by surveying a sampleofconsumers' buying habits or attemptingto predict future events. This might meanprojecting the future return of asecurityor asset class based on returnsinasample period.
6 YEAR NON-ENERGY1980 1361981 1391982 1441983 1241984 4301985 5671986 6761987 7001988 5981989 7491990 5611991 7721992 3241993 600DATA
7 FREQUENCY DISTRIBUTIONTABLESTEP 1: RANGE Range = maximum value − minimumvalue= 772 − 124 STEP 2: NUMBER OF CLASSNumber of class, k = 1 + 3.33 log n = 1 + 3.33 log 14 = 4.78 ≈ 5 STEP 3: CLASS INRERVAL Class interval = range k = 648 5 = 129.6 ≈ 130 STEP 4: CLASS BOUNDARYClass boundary = 254 − 253 2 =0.5 STEP 5: CLASS WIDTHClass width, C = upper boundary −lower boundary= 123.5 − 253.5 = 130
8
9
10 5.1 MEANANDMEDIANMEAN Mean, x = fx f = 6669 14 = 476.36 MEDIAN Median = f 2 th = 14 2 th = 7 = 4 Median = Lmo + N 2 − F fm C = 513.5 + 14 2 − 6 1 (130) = 546 NON- ENERGY FREQUENCY,f x fx CUMULATIVE FREQUENCY CLASS BOUNDARY 124-253 4 188.5 754 4 123.5-253.5 254-383 1 318.5 318.5 5 253.5-383.5 384-513 1 448.5 448.5 6 383.5-513.5 514-643 4 578.5 2314 10 513.5-643.5 644-733 4 798.5 2834 14 643.5-773.5 TOTAL = 14 = 6669
11 5.2 MODEMODE: 1 d1 = 4 − 0 = 4 d1 = 4 − 1 = 3 Mode = Lmo + d1 d1 + d2 C = 123.5 4 4 + 3 (130) = 197.79 MODE: 2 d1 = 4 − 1 = 3 d1 = 4 − 4 = 0 Mode = Lmo + d1 d1 + d2 C = 513.5 3 3 + 0 (130) = 643.5 MODE: 3 d1 = 4 − 4 = 0 d1 = 4 − 0 = 3 Mode = Lmo + d1 d1 + d2 C = 643.5 0 0 + 3 (130) = 643.5 NON- ENERGY FREQUENCY,f x fx CUMULATIVE FREQUENCY CLASS BOUNDARY 124-253 4 188.5 754 4 123.5-253.5254-383 1 318.5 318.5 5 253.5-383.5384-513 1 448.5 448.5 6 383.5-513.5514-643 4 578.5 2314 10 513.5-643.5644-733 4 798.5 2834 14 643.5-773.5TOTAL = 14 = 6669
12 5.3 MEAN DEVIATION, VARIANCEAND STANDARDDEVIATIONMEAN DEVIATION Mean deviation, E = x − x f f = 2674.28 14 = 191.02 VARIANCE Variance, 2 = − 2 = 592007.72 14 = 42286.27 STANDARD DEVIATIONStandard deviation = variance = 42286.27 = 205.64 NON- ENERGY FREQUENCY, f x fx |x − x| |x − x|f |x −x|2 f 124-253 4 188.5 754 287.86 1151.44 331453.52 254-383 1 318.5 318.5 157.86 157.86 24919.78 384-513 1 448.5 448.5 27.86 27.86 776.18 514-643 4 578.5 2314 102.14 408.56 41730.32 644-733 4 798.5 2834 232.14 928.56 215555.92 TOTAL = 14 = 6669 |x − x|f = 2674.28 |x −x|2 f = 592007.72
13 5.4 QUARTILE AND INTERQUARTILERANGE1 st QUARTILE Q1 = 1 4 × 14 = 3.5 ≈ 4 th = LQ1 + 1N 4 − F fQ1 C = 123.5 + 1(14) 4 − 0 4 130 = 237.25 3 rd QUARTILE Q3 = 3 4 × 14 = 10.5 ≈ 11 th = LQ3 + 3N 4 − F fQ3 C = 643.5 + 3(14) 4 − 10 4 130 = 659.75 INTERQUARTILE RANGE Interquartile range = Q3 − Q1 = 659.75 − 237.25 = 422.5 NON- ENERGY FREQUENCY,f x fx CUMULATIVE FREQUENCY CLASS BOUNDARY 124-253 4 188.5 754 4 123.5-253.5 254-383 1 318.5 318.5 5 253.5-383.5 384-513 1 448.5 448.5 6 383.5-513.5 514-643 4 578.5 2314 10 513.5-643.5 644-733 4 798.5 2834 14 643.5-773.5 TOTAL = 14 = 6669
14 5.5 DECILE ANDPERCENTILELOWER BOUNDARY Lower boundary = 254 − 0.5 = 253.5 6 th DECILE D6 = 6 10 × 14 = 8.4 ≈ 9 th D6 = LDK + 6N 10−F fDK C = 513.5 + 6(14) 10 − 6 4 130 = 591.5 32 nd PERCENTILE P32 = 32 100 × 14 = 4.48 ≈ 5 th P32 = LPK + 32N 100 − F fPK C = 253.5 + 32(14) 100 − 4 1 130 = 315.9 NON- ENERGY FREQUENCY,f x fx CUMULATIVE FREQUENCY CLASS BOUNDARY 124-253 4 188.5 754 4 123.5-253.5 254-383 1 318.5 318.5 5 253.5-383.5 384-513 1 448.5 448.5 6 383.5-513.5 514-643 4 578.5 2314 10 513.5-643.5 644-733 4 798.5 2834 14 643.5-773.5 TOTAL = 14 = 6669
15 HISTOGRAMGRAPHNON- ENERGY FREQUENCY,f x fx CUMULATIVE FREQUENCY CLASS BOUNDARY 124-253 4 188.5 754 4 123.5-253.5254-383 1 318.5 318.5 5 253.5-383.5384-513 1 448.5 448.5 6 383.5-513.5514-643 4 578.5 2314 10 513.5-643.5644-733 4 798.5 2834 14 643.5-773.5TOTAL = 14 = 6669 Histogram graph is a graph that displays thedataby using contiguous vertical bars of variousheights frequency of each class. In histogram graph, the peak of data or thetallest graph bar is the mode. Two or more peak of the data that have thesamehighest has two or more modes. Mode 1=197.75 Mode 2 &3=643.5
16 7.1 OGIVE GRAPH Ogive is a graph that represent thecumulative frequency for the classesinfrequency distribution table. It can be determined median, quartile, decile and percentile. In ogive graph a new class was addedwith frequency 0 MEDIANMedian = f 2 th = 14 2 th = 7 = 4 NON- ENERGY FREQUENCY,f CUMULATIVE FREQUENCY CLASS BOUNDARY 0-123 0 0 0-123.5 124-253 4 4 123.5-253.5 254-383 1 5 253.5-383.5 384-513 1 6 383.5-513.5 514-643 4 10 513.5-643.5 644-733 4 14 643.5-773.5 TOTAL = 14
17 7.2 QUARTILE1 st QUARTILE: Q1 = 1 4 × 14 = 3.5 ≈ 4 th 3 rd QUARTILE: Q3 = 3 4 × 14 = 10.5 ≈11 th
18 7.3 DECILE ANDPERCENTIL16 th DECILE: D6 = 6 10 × 14 = 8.4 ≈ 9 th 32 nd PERCENTILE: P32 = 32 100 ×14 = 4.48 ≈5 th
19 CONCLUSIONThe conclusion is based on a frequency distributiontable,the central tendency and dispersion, andalsographs. Our group was able to determine the total amount of non-energy produced in oil refineries from1980 to 1993 in Malaysia. We are able to measurethe mean, median, mode, mean deviation, variance, standard deviation, quartile, decile, and percentileby using a formula. Furthermore, our group is abletodraw graphs and find the quartile,decile, percentile, and median by using graphs. In the histogramgraph, the shape of the distribution graph is bimodal because it has two peaks. In the ogive graph, thecurve of the graph is concave up from1980 to 1993. This shows that the non-energy produced by oil refineries in Malaysia increased from1980 to 1993. There are several factors that influence the increasein non-energy production at oil refineries. Amongthem is a very high demand. In addition, thereareother factors that influence it, such as the current price drop, inflation, politics, and even trade policy. In order to maintain the rate of increase intheproduction of this product, the oil refinery companyneeds to ensure that non-energy productionissuitable according to current needs, quantity limits, and the market. In addition, the company alsoneedsto make preliminary preparations to face several constraints, such as disasters, pandemics, inflationrates, and the economy.
20 REFERENCE 1.BRITTANNICA PROBABILITY STATICS https://www.investopedia.com/terms/s/statistics.asp#:~:text=Statistics%20is%20a%20branch%20of,linear%20algebra%2C%20and%20probability%20theory. 2.US INFORMATION ENERGY ADMINISTRATIONhttps://makemeanalyst.com/explore-your-data-graphs- and-shapes-of-distributions/ 3.MAKE ME ANALYSIS https://www.eia.gov/energyexplained/oil-and-petroleum-products/refining-crude-oil-the-refining-process.php
21