Measures of Dispersion Study Guide: GED Math

Practice problems for these concepts can be found at:

Data Analysis, Statistics, and Probability Practice Problems: GED Math

Measures of Dispersion

Measures of dispersion, or the spread of a number set, can be in many different forms. The two forms that may appear on the GED are range and standard deviation.

Range

The range of a data set is the greatest measurement minus the least measurement. For example, given the values 5, 9, 14, 16, and 11, the range would be 16 – 5 = 11.

Standard Deviation

As you can see, the range is affected by only the two most extreme values in the data set. Standard deviation is a measure of dispersion that is affected by every measurement. To find the standard deviation of n measurements, follow these six steps:

1. First, find the mean of the measurements.
2. Find the difference between the mean and each measurement.
3. Square each of the differences.
4. Sum the square values.
5. Divide the sum by n.
6. Choose the nonnegative square root of the quotient.

When you find the standard deviation of a data set, you are finding the average distance from the mean for the n measurements. It cannot be negative, and when two sets of measurements are compared, the larger the standard deviation, the larger the dispersion.

Frequency Distribution

The frequency distribution is essentially the number of times, or how frequently, a measurement appears in a data set. It is represented by a chart like the one shown.

To use the chart, simply list each measurement only once in the x column and then write how many times it occurs in the f column.

Example

Show the frequency distribution of the following data set that represents the number of students enrolled in 15 classes at Middleton Technical Institute:

12, 10, 15, 10, 7, 13, 15, 12, 7, 13, 10, 10, 12, 7, 12

Be sure that the total number of measurements taken is equal to the total at the bottom of the frequency distribution chart.

Practice problems for these concepts can be found at:

Data Analysis, Statistics, and Probability Practice Problems: GED Math