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Chapter 22

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

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Chapter 22

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  1. Chapter 22 Business Statistics

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

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

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

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

  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. 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 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 49 49 = 3.1 16

  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 • Find median value of all employees • Find median value If Jane Hess ($27,000) were not on the payroll

  9. Finding the Median of a Group of Values Step 1. Orderly arrange values from the smallest to the largest Find the median value 95, 27, 32, 67, 40 • Step 2. Find the middle value • 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. 27, 32, 40, 67, 95 Find the median value 95, 32, 67, 40 32, 40, 67, 95 40 + 67 2 53.5

  10. Mode 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 3 is the mode since it is listed 4 times 3, 4, 5, 6, 3, 8, 9, 3, 5, 3

  11. Frequency Distribution A way of collecting and organizing raw data Price of Tally Frequency Computer $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 1 10,000 l 1 Computer costs Frequency distribution table

  12. Bar Graph Frequency of purchase 2000 4000 6000 8000 10000 Price of Computers

  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 Frequency of purchase $3,001- $5,000.99 $7,001- $9,000.99

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

  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. 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. Consumer Price Index (in percent) Table 22.1 Expense Atlanta Chicago NY LA Food 131.9 130.3 139.6 130.9 Housing 128.8 131.4 139.3 139.3 Clothing 133.8 124.3 121.8 126.4 Medical care 177.6 163.0 172.4 163.3

  18. Standard Deviation Intended to measure the spread of data around the mean Step 6. Find the square root ( ) of the number obtained in Step 5. This is the standard deviation Step 5. Divide the sum of the squared deviations by n - 1, where n equals the number of pieces of data Step 4. Sum all squared deviations Step 3. Square each deviation (multiply the deviation by itself) Step 2. Subtract the mean from each piece of data to find each deviation Step 1. Find the mean of the set of data

  19. Standard Deviation Step 1(1 + 2 + 5 + 10 + 12) = 6 (Mean) 5 Step 2Step 3 Data Data-Mean (Data-Mean) 1 1- 6 = -5 25 2 2 - 6 = -4 16 5 5 - 6 = -1 1 10 10 - 6 = 4 16 12 12 - 6 = 636 Total 0 94 (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 The standard deviation of data set A is 4.8

  20. Standard Deviation Step 1(4 + 4 + 5 + 8 + 9) = 6 (Mean) 5 Step 2Step 3 Data Data-Mean (Data-Mean) 1 4- 6 = -2 4 2 4 - 6 = -2 4 5 5 - 6 = -1 1 10 8 - 6 = 2 4 12 9 - 6 = 39 Total 0 22 (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 The standard deviation of data set A is 2.3

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