Chapter 9 Statistics, mean, median, mode, range

Math Statistics

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Chapter 9
Statistics

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9.1
Frequency Distributions;
Measures of Central
Tendency

3. 9 - 3
Example 1
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A survey asked a random sample of 30 business executives for
their recommendations as to the number of college credits in
management that a business major should have. The results are
shown below.
1) Group the data into intervals and find the frequency of each
interval.
2) Draw a histogram and frequency polygon

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Continue Example 1: Frequency Table

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Figure 1
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Find the mean of the following data: 12, 17, 21, 25, 27, 38, 49.
Solution:

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Example 2

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Find the mean of the following data: 12, 17, 21, 25, 27, 38, 49.
Solution:

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12 17 21 25 27 38 49
7
x
     

189
7

1 2
Let 12, 17, and so on. Here 7, since there are 7 numbers.x x n  
27
Example 2

9. 9 - 9

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Example 3
The table to the left lists the number of bankruptcy
petitions (in thousands) filed in the United States in the
years 2004–2009. Find the mean number of bankruptcy
petitions filed annually during this period. Source:
American Bankruptcy Institute.

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Example 3
The table to the left lists the number of bankruptcy
petitions (in thousands) filed in the United States in the
years 2004–2009. Find the mean number of bankruptcy
petitions filed annually during this period. Source:
American Bankruptcy Institute.

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Find the mean for the data shown in the following frequency
distribution.
Example 4

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Find the mean for the data shown in the following frequency
distribution.
Example 4

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Find the mean of the following grouped frequency.
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Example 5

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Find the mean of the following grouped frequency.
IntervalMidpoint, x Frequency fProduct x f
0-6 3 2 6
7-13 10 4 40
14-20 17 7 119
21-27 24 10 240
28-34 31 3 93
35-41 38 1 38
Total = 27Total = 536
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Example 5

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Median

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Find the median of the data 12, 17, 21, 25, 27, 38, 49.
Solution:
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Example 6

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Solution: The median is the middle number; in this case, 25. (Note
that the numbers are already arranged in numerical order.) In this
list, three numbers are smaller than 25 and three are larger.
12, 17, 21, 25, 27, 38, 49.
6 (c) Find the median for each list of numbers 47, 59, 32, 81, 74, 153.
Solution: First arrange the numbers in numerical order, from
smallest to largest 32, 47, 59, 74, 81, 153.
There are six numbers here; the median is the mean of the two
middle numbers.
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59 74 133 1
Median 66
2 2 2

  
Continue Example 6

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Example 7: Mode
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Find the mode for each list of numbers.
(a)57, 38, 80, 55,55, 87, 98, 55, 57
The most frequent entry (data occurs) is Mode.

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Seeds that are dried, placed in an airtight container, and stored in a cool,
dry place remain ready to be planted for a long time. The table below gives
the amount of time that each type of seed can be stored and still remain
viable for planting.
Find the mean, median, and mode of the information in the table.
Example 8

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Example 8
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9.2
Measures of Variation

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Range
The difference between the largest and
smallest number in a sample is called the
range
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Example 8
Find the range for each list of numbers.
(a)12, 27, 6, 19, 38, 9, 42, 15
(b)74, 112, 59, 88, 200, 73, 92, 175
(c)See table
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25. 9 - 25
Example 8
Find the range for each list of numbers.
(a)12, 27, 6, 19, 38, 9, 42, 15
Solution: 36
(a)74, 112, 59, 88, 200, 73, 92, 175
Solution: 141
(a)See table
Solution: Range for sample I is 3, Sample II is 0 and Sample III is 10.
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Deviation from the Mean
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Find the mean, variance and standard deviation of the following
numbers
7, 9, 18, 22, 27, 29, 32, 40.
Example 9

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Example 9

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Find the mean, variance and standard deviation of the following
numbers
Example 10

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Find the mean, variance and standard deviation of the following
numbers
Example 10

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