Kinh tế học - Chapter 22: Business statistics

Chapter 22Business StatisticsDefine and calculate the meanExplain and calculate a weighted meanDefine and calculate the medianDefine and identify the modeBusiness Statistics#22Learning Unit ObjectivesMean, Median, and ModeLU22.1Prepare a frequency distributionPrepare bar, line, and circle graphsCalculate price relatives and cost comparisonsBusiness Statistics#22Learning Unit ObjectivesFrequency Distributions and GraphsLU22.2Explain and calculate the rangeDefine and calculate the standard deviationEstimate percentage of data by using standard deviationsBusiness Statistics#22Learning Unit ObjectivesMeasures of Dispersion (Optional Section)LU22.3Mean - Average used to indicate a single value that represents an entire group of numbersMedian - A measurement that indicates the center of the data (Average)TerminologyMode - a measurement that records values. The value that occurs most oftenMeanMean = Sum of all values Number of valuesThe accountant of Bill’s Sport Shop told Bill, the owner, that the average daily sales for the week were $150.14. The accountant stressed that $150.14 was an average and did not represent specific daily sales. Bill wanted to know how the accountant arrived at $150.14.Sun. Mon. Tues. Wed. Thur. Fri. Sat. $400 $100 $68 $115 $120 $68 $180Mean = $400 + $100 + $68 + $115 + $120 +$68 + $180 = $150.14 7Weighted MeanWeighted Mean = Sum of products Sum of frequenciesHow Jill Rivers calculated her GPA to the nearest tenth. Credit Grade PointsCourses attempted received (Credits x Grade)Intro to Comp 4 A 16 (4 x 4)Psychology 3 B 9 (3 x 3)English Comp. 3 B 9 (3 x 3)Business Law 3 C 6 (2 x 3)Business Math 3 B 9 (3 x 3) 16 4949 = 3.116Finding the Median of a Group of ValuesLook below at the following yearly salaries of the employees of Rusty’s Clothing Shop.Alice Knight $95,000 Jane Wang $67,000Jane Hess $27,000 Bill Joy $40,000Joel Floyd $32,000Find median value of all employeesFind median value If Jane Hess ($27,000) were not on the payrollFinding the Median of a Group of ValuesStep 1. Orderly arrange values from the smallest to the largestStep 2. Find the middle valueOdd number of values: Median is the middle value. Divide the total number of numbers by 2. (5/2 = 2 ½). The next-higher number is the median.B. Even number of values: Median is the average of the two middle values.Find the median value 95, 27, 32, 67, 40 27, 32, 40, 67, 9532, 40, 67, 95 40 + 67 2 53.5Find the median value 95, 32, 67, 40 Mode3, 4, 5, 6, 3, 8, 9, 3, 5, 33 is the mode since it is listed 4 timesThe value that occurs most oftenIf two or more numbers appear most often, you may have two or more modes.If all the values are different, there is no modeFrequency DistributionA way of collecting and organizing raw dataPrice of Tally FrequencyComputer$1,000 llll 5 2,000 l 1 3,000 llll 5 4,000 l 1 5,000 ll 2 6,000 ll 2 7,000 l 1 8,000 l 1 9,000 l 110,000 l 1Frequency distribution table100070004000100050001000300050002000300030003000800090003000600060001000100001000Computer costsBar GraphFrequency of purchasePrice of Computers200040008000100006000Bar GraphClass Frequency$1000 - $ 3,000.99 11$3001 - 5,000.99 3$5001 - 7,000.99 3$8001 - 9,000.99 2$9001 - 11,000.99 1$3,001-$5,000.99$7,001-$9,000.99Frequency of purchaseCircle Graph12.9%12.9%56.9%17.3%Revenues1st Qtr. $20,4002nd Qtr $27,4003rd Qtr $90,0004th Qtr $20,400Measure of DispersionMeasure of Dispersion – a number that describes how the numbers of a set of data are spread out or dispersed.Range – The difference between the two extreme values (highest and lowest) in a group of values or a set of data.Range = Highest value – Lowest valueFind the range of the following values:83.6, 77.3, 69.2, 93.1, 85.4, 71.6Range = 93.1 – 69.2 = 23.9Index NumbersPrice relative = Current price x 100 Base year’s priceA calculator may cost $9 today relative to a cost of$75 some 30 years ago. What is the relative price? $9 x 100 = .12 = 12%$75Consumer Price Index (in percent)Expense Atlanta Chicago NY LAFood 131.9 130.3 139.6 130.9Housing 128.8 131.4 139.3 139.3Clothing 133.8 124.3 121.8 126.4Medical care 177.6 163.0 172.4 163.3Table 22.1Step 1. Find the mean of the set of dataStep 2. Subtract the mean from each piece of data to find each deviation Step 3. Square each deviation (multiply the deviation by itself)Step 4. Sum all squared deviationsStep 5. Divide the sum of the squared deviations by n - 1, where n equals the number of pieces of dataStep 6. Find the square root ( ) of the number obtained in Step 5. This is the standard deviationIntended to measure the spread of data around the meanStandard DeviationStep 1 (1 + 2 + 5 + 10 + 12) = 6 (Mean) 5 Step 2 Step 3Data Data-Mean (Data-Mean)1 1- 6 = -5 252 2 - 6 = -4 165 5 - 6 = -1 110 10 - 6 = 4 1612 12 - 6 = 6 36 Total 0 94 (Step 4)Step 5: Divide by n-1: 94 = 94 = 23.5 5-1 4Step 6: The square root of 23.5 is 4.8 Data Set A x x x x x0 1 2 3 4 5 6 7 8 9 10 11 12 13 Standard DeviationThe standard deviation of data set A is 4.8Step 1 (4 + 4 + 5 + 8 + 9) = 6 (Mean) 5 Step 2 Step 3Data Data-Mean (Data-Mean)1 4- 6 = -2 42 4 - 6 = -2 45 5 - 6 = -1 110 8 - 6 = 2 412 9 - 6 = 3 9 Total 0 22 (Step 4)Step 5: Divide by n-1: 22 = 22 = 5.5 5-1 4Step 6: The square root of 5.5 is 2.3 Data Set B x x x x x0 1 2 3 4 5 6 7 8 9 10 11 12 13 Standard DeviationThe standard deviation of data set A is 2.3