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• How do I find
measures of central
tendency and
dispersions?
7.3
Find Measures of Central Tendency and Dispersion
Example 1 Find measures of central tendency
Quiz Scores
Find the mean, median, and mode of the data
set.
19, 15, 22,
17, 21, 17,
25, 18, 17
Solution
To find the mean, divide the sum of the scores by the number
of scores.
19  15    17
x
9
__________
__________
__________
_____
171
19

 ____
9
__________
_
To find the median, first order the quiz scores from least to
greatest.
15, 17, 17, 17, 18, 19, 21, 22, 25
__________
__________
___
Because there is an odd number of scores, the median is the
middle number, _____.
18
There is one mode, _____,
17 because this number occurs most
frequently.
7.3
Find Measures of Central Tendency and Dispersion
Checkpoint. Complete the following exercise.
1. The data set below gives the recorded speeds (in mi/h) of
10 different cars on a local highway during a week day.
69, 62, 64, 67, 62, 64, 63, 65, 60, 64
Find the mean, median and mode of the data set.
69  62  64  67  62  64  63  65  60  64
x
10
x  64
60, 62, 62, 63, 64, 64, 64, 65, 67, 69
Median: 64
Mode: 64
7.3
Find Measures of Central Tendency and Dispersion
Standard Deviation of a Data Set
The standard deviation s (read as “sigma”) of
x1, x2, . . ., xn is
s
x1  x   x2  x 
2
2
n
   xn  x 
2
7.3
Find Measures of Central Tendency and Dispersion
Example 2 Find measures of dispersion
Find the range and standard deviation for the
quiz scores in Example 1.
Solution
Quiz Scores
19, 15, 22,
17, 21, 17,
25, 18, 17
To find the range, subtract the least data value from the
greatest data value.
Range  ____
10
15  ____
25  ____
To find the standard deviation, substitute the scores and the
mean into the formula.
s
15  19   317  19   25  19
2
2
 ____
2.9
___
9
2
Find Measures of Central Tendency and Dispersion
7.3
Example 3 Compare data sets
The lists show the number of memberships sold each month for one year
by two competing athletic clubs. Compare the mean and standard
deviation for the numbers of memberships sold by the two athletic clubs.
Club A: 12, 9, 14, 6, 10, 11, 19, 6, 17, 11, 4, 13
Club B: 17, 10, 22, 15, 14, 19, 4, 8, 12, 22, 20, 5
Solution
12  9    13 132
Club A: Mean:
x

12
__________
__________
____
12
 ____
11
_________
Std. Dev.:
s
12  11  9  11   13  11
 ____
4.3
2
2
___
12
2
7.3
Find Measures of Central Tendency and Dispersion
Example 3 Compare data sets
The lists show the number of memberships sold each month for one year
by two competing athletic clubs. Compare the mean and standard
deviation for the numbers of memberships sold by the two athletic clubs.
Club A: 12, 9, 14, 6, 10, 11, 19, 6, 17, 11, 4, 13
Club B: 17, 10, 22, 15, 14, 19, 4, 8, 12, 22, 20, 5
Solution
17  10    5 168
Club B: Mean:
Std. Dev.:
s
 ____
6.0
x

12
__________
__________
____
17  14   10  14
2
2
12
 ____
14
_________
  5  14 
2
___
12
Athletic Club ___
B has a greater mean and a greater standard
deviation than Athletic Club ____.
A
7.3
Find Measures of Central Tendency and Dispersion
Checkpoint. Complete the following exercise.
2. Find the range and standard deviation of the data set in
Exercise 1.
69, 62, 64, 67, 62, 64, 63, 65, 60, 64
Range: 69 – 60 = 9
s
60  64  262  64
s  2.4
2
2
10
  69  64
2
7.3
Find Measures of Central Tendency and Dispersion
Checkpoint. Complete the following exercise.
3. Compare the means and standard deviations of Set A and
Set B.
Set A
Set B
4
2
7
6
5
5
9
4
10
3
4  7  5  9  10
265 43
xA 
xB 

4

7
5
5
sA 
sB 
4  7   7  7   5  7   9  7   10  7 2
2
2
2
2
5
2
2
2
2
2



4

4
 3  4
2  4  6  4  5  4
5
 2.3
 1.4
Set A has a greater mean and standard deviation than Set B.
7.3
Find Measures of Central Tendency and Dispersion
Pg. 272, 7.3 #1-13