• Calculate the standard deviation of a set of data.
• Determine what percent of a set of data fall within one (two, three) standard deviations of the mean.

• measures of dispersion
• deviation from the mean
• variance
• standard deviation

s 2 
  x  x  2 n  1 variance (ungrouped data) s  s 2 standard deviation

s 2  n
1
 1



 x 2 
  n x 2



 alternate variance
(ungrouped data) s 2  n
1
 1



  f  x 2


  f n
 x 2



 alternate variance for grouped data where x is the midpoint of the group and n is the sum of the frequencies

1. 50 50 50 50 50
2. 46 50 50 50 54
3. 5 50 50 50 95

The weight (in pounds) of the ten
Truly Amazing Dudes are as follows:
152 196 144 139 166
83 186 157 140 138 a. Find the mean and standard deviation of the weights.
What percent of the data lies within one standard deviation of the mean?

According to m&m-Mars blue m&ms should make up 10% of the m&ms in each plain m&m package. Below are the percent of blue m&ms for 6 packages of plain m&ms. Find the mean, the variance, and standard deviation of the percent of blue m&ms in these 6 packages.
15% 14% 17% 28% 16% 17%

The table below shows the price per gallon of regular unleaded gasoline in Tempe (in the dark ages).
Price number of gas stations
How many stations are selling gas at a price that is within one standard deviation of the mean?
1.11
1.13
1.23
1.24
1.35
3
5
10
9
6
1.45
2

The ages of over 52 million women who gave birth in the United States between
June 1987 and June 1988 are given in the table below. Find the standard deviation of the ages of these women.
x = age
18 ≤ x < 25
25 ≤ x < 30
30 ≤ x < 35
35 ≤ x < 40
40 ≤ x < 45 number of women
13167000
10839000
10838000
9586000
8155000