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Chapter 22
Business Statistics
1-2
McGraw-Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.
#22
Business Statistics
Learning Unit Objectives
LU22.1 Mean, Median, and Mode
1-3
•
Define and calculate the mean
•
Explain and calculate a weighted mean
•
Define and calculate the median
•
Define and identify the mode
Terminology
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
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Median - A measurement
that indicates the center of
the data (Average)
Mean
Mean = Sum of all values
Number of values
What is the mean of the following daily sales?
Mon
Tues
Wed. Thur. Fri.
Sat.
$200
$325
$570
$950
$711
$880
Mean = $200 + $325 + $570 + $711 + $880 +$950 = $606
6
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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 = 3.08
13
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Finding the Median of a Group of Values
Step 1. Orderly arrange values
from the smallest to the largest
Find the median age
42, 35, 87, 23, 50
Step 2. Find the middle value
23, 35, 42, 50, 87
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.
Find the median age
42, 35, 87, 50
B. Even number of
values: Median is the average of
the two middle values.
35, 42, 50, 87
42 + 50
2
46
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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
6, 8, 0, 3, 4, 23, 57, 31, 22,
47, 31, 2, 6, 9, 31
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31 is the
mode
since it is
listed 3
times
Find Mean, Median, Mode
• Here are the monthly rainfall totals for the past year:
•
•
•
•
•
•
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2.4; 1.9; 3.7; 4.2; 3.4; 2.7; 1.7; 1.9; .8; 2.1; .7; 2.3
Calculate the monthly Mean:
30.2 / 12 = 2.52
Find the Median:
.7 .8 1.7 1.9 1.9 2.1 2.3 2.4 2.7 3.4 3.7 4.2
What is the Mode:
1.9
#22
Business Statistics
Learning Unit Objectives
LU22.2 Frequency Distributions and Graphs
1-10
•
Prepare a frequency distribution
•
Prepare bar, line, and circle graphs
•
Calculate price relatives and cost comparisons
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
1
2
3
4
5
6
7
8
9
10
11
l
l
ll
ll
lll
l
l
ll
l
l
l
1
1
0
2
2
3
1
1
2
1
1
1
Frequency
distribution table
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Bar Graph
Frequency of
consumption
4
3
2
1
0
0
1
2
3
4
5
6
7
8
Number of drinks
1-12
9
10 11
Line Graph
$17,000
$16,000
$15,000
$14,000
$13,000
$12,000
$11,000
$10,000
$9,000
$8,000
1995
1996
1997
Year
1-13
1998
1999
2000
Circle Graph
12.9%
12.9%
17.3%
56.9%
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Revenues
1st Qtr
$20,400
2nd Qtr $27,400
3rd Qtr $90,000
4th Qtr $20,400
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INDEX NUMBERS
• Use to compare when values (prices) change over time
• May be used to compare geographically diverse values
• Commonly associated with the CPI (consumer price
index)
• Express relative changes over time in relation to a base
• Public Data Query
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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
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#22
Business Statistics
Learning Unit Objectives
LU22.3 Measures of Dispersion (Optional Section)
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•
Explain and calculate the range
•
Define and calculate the standard deviation
•
Estimate percentage of data by using standard
deviations
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
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Standard Deviation
Step 1 (1 + 2 + 5 + 10 + 12) = 6
5
Data
1
xx
x
x
x
2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 5
10
12
Data set
Step 2
Step 3
Data-Mean
1- 6 = -5
2 - 6 = -4
5 - 6 = -1
10 - 6 = 4
12 - 6 = 6
Total 0
(Data-Mean)
25
16
1
16
36
94 (Step 4)
Step 5: Divide by n-1: 94 = 94 = 23.5
5-1
4
Step 6: The square root of
1-19
23.5 is 4.8