whole numbers; how to dissect and solve word problemsstaff · weighted mean weighted mean = sum of...
TRANSCRIPT
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
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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
22-12
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