Measures of Dispersion

1
Measures of Dispersion
2
Objectives

• 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.

3
Vocabulary

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

4
Formulas
variance (ungrouped data)
standard deviation
5
Alternate Formulas
alternate variance (ungrouped data)
alternate variance for grouped data where x is
the midpoint of the group and n is the sum of the
frequencies
6
Find the mean and standard deviation of each set
of data below

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

7
The weight (in pounds) of the ten Truly Amazing
Dudes are as follows
152 196 144 139 16683 186 157 140 138

1. Find the mean and standard deviation of the
   weights.What percent of the data lies within one
   standard deviation of the mean?

8
According to mm-Mars blue mms should make up
10 of the mms in each plain mm package. Below
are the percent of blue mms for 6 packages of
plain mms. Find the mean, the variance, and
standard deviation of the percent of blue mms in
these 6 packages.15 14 17 28 16 17
9
The table below shows the price per gallon of
regular unleaded gasoline in Tempe (in the dark
ages).
Price number of gas stations
1.11 3
1.13 5
1.23 10
1.24 9
1.35 6
1.45 2
How many stations are selling gas at a price that
is within one standard deviation of the mean?
10
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 number of women
18 x lt 25 13167000
25 x lt 30 10839000
30 x lt 35 10838000
35 x lt 40 9586000
40 x lt 45 8155000