22-1

Chapter 22

Business Statistics

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

22-2

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

Terminology

Mode - a measurement that

records values. The value that

occurs most often

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Mean

Mean = Sum of all valuesNumber 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 = $150.147

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How is your GPA calculated?

• A=4 grade points for each unit

• B=3 grade points for each unit

• C=2 grade points for each unit

• D=1 grade point for each unit

• F=0 grade points for each unit

• This is why an A in a 5-unit foreign language class

is worth five times more than an A in

a 1-unit physical education class.

Spanish 5 units x 4 grade points

P.E. 1 unit x 4 grade points

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Weighted Mean

Weighted Mean = Sum of productsSum 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

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Finding the Median of a Group of Values

Step 1. Orderly arranged 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 + 502

46

Find the median age

42, 35, 87, 50

22-7

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

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Frequency Distribution

A way of collecting and

organizing raw data

The average amount of

Starbucks 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

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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 Starbucks drinks

Used to compare quantities

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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

Year

Used to show progress over time

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Circle Graph

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

12.9%12.9%

56.9%

17.3%

Revenues

1st Qtr $20,400

2nd Qtr $27,400

3rd Qtr $90,000

4th Qtr $20,400Used to illustrate percents

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Index Numbers

Price relative = Current price x 100Base 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

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Consumer Price Index (in percent)

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

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Standard Deviation

• Find the mean of the set of data

• Subtract the mean from each piece of data to find each

deviation

• Square each deviation (multiply the deviation by itself)

• Sum all squared deviations

• Divide the sum of the squared deviations by n - 1, where n

equals the number of pieces of data

• Find the square root √ of the number obtained in the

previous step.

Intended to measure the spread of data around the mean

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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 = 23.55-1 4

Step 6: The square root of 23.5 is 4.8

Data set

x x x x x

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Standard Deviation