22-1

22-2

Chapter 22Chapter 22

Business StatisticsBusiness Statistics

McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

22-3

• Define and calculate the mean

• Explain and calculate a weighted mean

• Define and calculate the median

• Define and identify the mode

Business Statistics#22#22Learning Unit ObjectivesMean, Median, and ModeLU22.1LU22.1

22-4

• Prepare a frequency distribution

• Prepare bar, line, and circle graphs

• Calculate price relatives and cost comparisons

Business Statistics#22#22Learning Unit ObjectivesFrequency Distributions and GraphsLU22.2LU22.2

22-5

• Explain and calculate the range

• Define and calculate the standard deviation

• Estimate percentage of data by using standard deviations

Business Statistics#22#22Learning Unit ObjectivesMeasures of Dispersion (Optional Section)

LU22.3LU22.3

22-6

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

22-7

Mean

Mean = Sum of all values Number of values

What is the mean of the following daily sales?

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

22-8

Weighted Mean

Weighted Mean = Sum of products Sum of frequencies

What is the weighted mean (GPA) for the student?

Credit Grade Points

Courses attempted received (Credits x Grade)Business Math 3 B 9 (3 x 3)Speech 3 C 6 (3 x 2)Accounting 4 A 16 (4 x 4)English 3 B 9 (3 x 3)

13 40

40 = 3.0813

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. The next-higher number is the median.

B. Even number of values: Median is the average of the two middle values.

Find the median age 42, 35, 87, 23, 50

23, 35, 42, 50, 87

35, 42, 50, 87

42 + 50 2

46

Find the median age 42, 35, 87, 50

22-10

Mode

6, 8, 0, 3, 4, 23, 57, 31, 22, 47, 31, 2, 6, 9, 31

31 is the mode

since it is listed 3 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

22-11

Frequency Distribution

A way of collecting and organizing raw data

The average amount of alcoholic beverages consumed per week

5 7 8 4

3 5 8 3

1 6 10 4

9 11 5 0

Drinks Tally Frequency

0 l 11 l 12 - 03 ll 24 ll 25 lll 36 l 17 l 18 ll 29 l 110 l 111 l 1

Frequency distribution table

22-12

Bar Graph

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9 10 11

Fre

qu

ency

of

con

sum

pti

on

Number of drinks

22-13

Line Graph

$8,000

$9,000

$10,000

$11,000

$12,000

$13,000

$14,000

$15,000

$16,000

$17,000

1999 2000 2001 2002 2003 2004

Ave

rage

cos

t of

Col

lege

tu

itio

n

Year

22-14

Circle Graph

1st Qtr2nd Qtr3rd Qtr4th Qtr

12.9%12.9%

56.9%

17.3%

Revenues

1st Qtr $20,400

2nd Qtr $27,400

3rd Qtr $90,000

4th Qtr $20,400

22-15

Index Numbers

Price relative = Current price x 100 Base year’s price

A computer cost $850 today relative to a cost of $1,300 some 5 years ago. What is the relative price?

$850 x 100 = 65.38 = 65.4$1,300

22-16

Consumer Price Index (in percent)

Expense Atlanta Chicago NY LA

Food 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 177.6 163.0 172.4 163.3

22-17

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

22-18

Step 1 (1 + 2 + 5 + 10 + 12) = 65

Step 2 Step 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 = 6 36

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

x x x x x0 1 2 3 4 5 6 7 8 9 10 11 12 13

Standard Deviation