1. McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved Chapter 22 Business Statistics

2. 22-2 1. Define and calculate the mean 2. Explain and calculate a weighted mean 3. Define and calculate the median 4. Define and identify the mode Business Statistics #22 Learning Unit Objectives Mean, Median, and Mode LU22.1

3. 22-3 1. Prepare a frequency distribution 2. Prepare bar, line, and circle graphs 3. Calculate price relatives and cost comparisons Business Statistics #22 Learning Unit Objectives Frequency Distributions and Graphs LU22.2

4. 22-4 1. Explain and calculate the range 2. Define and calculate the standard deviation 3. Estimate percentage of data by using standard deviations Business Statistics #22 Learning Unit Objectives Measures of Dispersion (Optional Section) LU22.3

5. 22-5 Mean - Average used to indicate a single value that represents an entire group of numbers Median - A measurement that indicates the center of the data (Average) Terminology Mode - a measurement that records values. The value that occurs most often

6. 22-6 Mean Mean = Sum of all values Number of values The 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$180 Mean = $400 + $100 + $68 + $115 + $120 +$68 + $180 = $150.14 7

7. 22-7 Weighted Mean Weighted Mean = Sum of products Sum of frequencies How Jill Rivers calculated her GPA to the nearest tenth. Credit Grade Points Courses attempted received (Credits x Grade) Intro to Comp4 A 16 (4 x 4) Psychology3 B 9 (3 x 3) English Comp.3 B 9 (3 x 3) Business Law3 C 6 (2 x 3) Business Math3 B9 (3 x 3) 16 49 49 = 3.1 16

8. 22-8 Finding the Median of a Group of Values Look below at the following yearly salaries of the employees of Rusty’s Clothing Shop. Alice Knight $95,000 Jane Wang $67,000 Jane Hess $27,000 Bill Joy $40,000 Joel Floyd $32,000 1.Find median value of all employees 2.Find median value If Jane Hess ($27,000) were not on the payroll

9. 22-9 Finding the Median of a Group of Values Step 1. Orderly arrange values from the smallest to the largest Step 2. Find the middle value A.Odd 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, 95 32, 40, 67, 95 40 + 67 2 53.5 Find the median value 95, 32, 67, 40

10. 22-10 Mode 3, 4, 5, 6, 3, 8, 9, 3, 5, 3 3 is the mode since it is listed 4 times The value that occurs most often If two or more numbers appear most often, you may have two or more modes. If all the values are different, there is no mode

11. 22-11 Frequency Distribution A way of collecting and organizing raw data Price of Tally Frequency Computer $1,000 llll5 2,000 l1 3,000 llll5 4,000 l1 5,000 ll2 6,000 ll2 7,000 l1 8,000 l1 9,000 l1 10,000 l1 Frequency distribution table 1000700040001000500010003000 500020003000 80009000 30006000 1000100001000 Computer costs

12. 22-12 Bar Graph Frequency of purchase Price of Computers 200040008000100006000

13. 22-13 Bar Graph Class 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- $9,000.99 Frequency of purchase

14. 22-14 Circle Graph 12.9% 56.9% 17.3% Revenues 1 st Qtr. $20,400 2nd Qtr $27,400 3rd Qtr $90,000 4th Qtr $20,400

15. 22-15 Measure of Dispersion Measure 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 value Find the range of the following values: 83.6, 77.3, 69.2, 93.1, 85.4, 71.6 Range = 93.1 – 69.2 = 23.9

16. 22-16 Index Numbers Price relative = Current price x 100 Base year’s price A 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% $75

17. 22-17 Consumer Price Index (in percent) Expense Atlanta Chicago NY LA Food131.9130.3139.6130.9 Housing128.8131.4139.3139.3 Clothing133.8124.3121.8126.4 Medical care177.6163.0172.4163.3 Table 22.1

18. 22-18 Step 1. Find the mean of the set of data Step 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 deviations Step 5. Divide the sum of the squared deviations by n - 1, where n equals the number of pieces of data Step 6. Find the square root ( ) of the number obtained in Step 5. This is the standard deviation Intended to measure the spread of data around the mean Standard Deviation

19. 22-19 Step 1 (1 + 2 + 5 + 10 + 12) = 6 (Mean) 5 Step 2Step 3 DataData-Mean(Data-Mean) 11- 6 = -525 22 - 6 = -416 55 - 6 = -1 1 1010 - 6 = 416 1212 - 6 = 636 Total 094 (Step 4) Step 5: Divide by n-1: 94 = 94 = 23.5 5-1 4 Step 6: The square root of 23.5 is 4.8 Data Set A x x x x x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Standard Deviation The standard deviation of data set A is 4.8

20. 22-20 Step 1 (4 + 4 + 5 + 8 + 9) = 6 (Mean) 5 Step 2Step 3 DataData-Mean(Data-Mean) 14- 6 = -2 4 24 - 6 = -2 4 55 - 6 = -1 1 108 - 6 = 2 4 129 - 6 = 3 9 Total 022 (Step 4) Step 5: Divide by n-1: 22 = 22 = 5.5 5-1 4 Step 6: The square root of 5.5 is 2.3 Data Set B x x x x x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Standard Deviation The standard deviation of data set A is 2.3