Sometimes data is given in a frequency table. Many calculators that can calculate standard deviation from a list can also calculate standard deviation from a frequency table.

Example 2

The number of goals scored in each game played in the 2011–2012 NHL season is shown for the Calgary Flames and the Edmonton Oilers.

Goals
Scored		Calgary Flames
Frequency		Edmonton Oilers
Frequency
0
6
6
1
23
13
2
16
27
3
16
21
4
10
5
5
8
3
6
2
5
7
1
0
8
0
1
9
0
1
Source: www.nhl.com


  1. Determine the mean and standard deviation of the data for each team.

    Many calculators allow you to input a frequency table to determine the mean and standard deviation of a data set. You may need to check your calculator's instructions for assistance. Directions for determining the mean and standard deviation using a TI-83 / TI-84 calculator can be found in Equipment Room or by clicking here.

    Calgary Flames: Edmonton Oilers:

  2. What can you conclude about each team's performance in the 2011–2012 season?

    The Edmonton Oilers' mean was higher, so they tended to score more goals each game. Calgary's standard deviation was lower, which means they were more consistent and therefore more likely than Edmonton to score near their mean number of goals in a game.


Example 3

Estimate the mean and standard deviation of the following distribution.

The exact heights of the people are not known, however, using the middle value of each class will provide a reasonable estimate of the mean and standard deviation.

Height EstimateFrequency
107.5
3
122.5
9
137.5
25
152.5
27
167.5
20
182.5
8
197.5
1

Use technology to determine the mean and standard deviation.

The mean is approximately 150 and the standard deviation is approximately 19.