MAT 142 Lecture Video Series

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 deviation

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

Find the mean and standard deviation of each set of data below:

The weight (in pounds) of the ten Truly Amazing Dudes are as follows: a.Find the mean and standard deviation of the weights. b.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%

Price number of gas stations 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 two standard deviations of the mean?

AgeNumber of Women 15 ≤ x  20442, ≤ x  251,081, ≤ x  301,812, ≤ x  35950, ≤ x  40499, ≤ x  45105, ≤ x  507,000 The ages of the women who gave birth in the United States in 2006 are given in the table below. Find the standard deviation of the ages of these women.

Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University