Measures of Dispersion

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.

Vocabulary

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

Formulas

variance (ungrouped data)

standard deviation2ss

1

2

2

n

xxs

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

n

xfxf

ns

2

22

11

n

xx

ns

2

22

11

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

The weight (in pounds) of the ten Truly Amazing Dudes are as follows:

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

152 196 144 139 16683 186 157 140 138

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%

Pricenumber of gas

stations

1.11 3

1.13 5

1.23 10

1.24 9

1.35 6

1.45 2

The table below shows the price per gallon of regular unleaded gasoline in Tempe (in the dark ages).

How many stations are selling gas at a price that is within one standard deviation of the mean?

x = age number of women

18 ≤ x < 25 13167000

25 ≤ x < 30 10839000

30 ≤ x < 35 10838000

35 ≤ x < 40 9586000

40 ≤ x < 45 8155000

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.