1. Chapter 22
Statistics

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

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

4. Learning Unit Objectives
#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
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

7. 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)
Intro to Comp 4 A (4 x 4)
Psychology B 9 (3 x 3)
English Comp B (3 x 3)
Business Law C (2 x 3)
Business Math 3 B 9 (3 x 3)
49 = 3.1 16

8. Finding the Median of a Group of Values
Step 1. Orderly arrange values from the smallest to the largest
Find the median age , 35, 87, 23, 50
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.
23, 35, 42, 50, 87
Find the median age , 35, 87, 50
35, 42, 50, 87 2 46

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

10. Frequency Distribution
A way of collecting and organizing raw data
Price of Tally Frequency
Computer
$1, llll 5
2, l 1
3, llll 5
4, l 1
5, ll 2
6, ll 2
7, l 1
8, l 1
9, l 1
10, l 1
Computer costs
1000
7000
4000
5000
3000
2000
8000
9000
6000
10000
Frequency distribution table

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

12. Bar Graph Class Frequency $1000 - $ 3,000.99 11 $3001 - 5,000.99 3
$ $ 3,
$ ,
$ ,
$ ,
$ ,
Frequency of purchase
$3,001-
$5,000.99
$7,001-
$9,000.99

13. Average cost of College
Line Graph
Average cost of College
tuition
Year

14. Circle Graph Revenues 1st Qtr. $20,400 2nd Qtr $27,400 3rd Qtr $90,000
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. Find the range of the following values:
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 computer cost $850 today relative to a cost of $1,300 some 5 years ago. What is the relative price?
$850 x = = 65.4
$1,300

17. Consumer Price Index (in percent)
Expense Atlanta Chicago NY LA
Food
Housing
Clothing
Medical care

18. Intended to measure the spread of data around the mean
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 Data Set A x x x x x
Step 1 ( ) = 6 (Mean) 5
Step 2 Step 3
Data Data-Mean (Data-Mean) = = =
= 4 16
= 6 36
Total (Step 4)
Step 5: Divide by n-1: = = 23.5
Step 6: The square root of is 4.8
Data Set A
x x x x x
The standard deviation of data set A is 4.8

20. Standard Deviation Data Set B x x x x x
Step 1 ( ) = 6 (Mean) 5
Step 2 Step 3
Data Data-Mean (Data-Mean) = = = = =
Total (Step 4)
Step 5: Divide by n-1: = = 5.5
Step 6: The square root of is 2.3
Data Set B x
x x x x
The standard deviation of data set A is 2.3

21. Problem 22-19
.35 x 360 = 126
.28 x 360 = 100.8
.20 x 360 = 72
.17 x 360 = 61.2
Misc. 17%
Transportation 35%
Food and entertainment %
Hotel 28%

22. Problem 22-20 Frequency $0- $5.99 5 5 $6- $11.99 3 3 $12- $17.99 4 4
Intervals Tally Frequency
$0- $
$6- $
$12- $
$18- $

23. Problem 22-21 Tally Day Bagels Product 150 9 9 x 150 = 1,350
7, 510
7,510/ 30 = = 250 Bagels

24. Problem 22-22
Thousands of dollars