Warm Up
A measure of central tendency is a measure of the "centre" of a data set. Previously, you used the mean (arithmetic mean), median, and mode as measures of central tendency. The arithmetic mean is determined by adding all values in a data set and dividing the sum by the number of values in the set.
The median is determined by ordering the data from smallest to largest and identifying the middle value. If there is an even number of data points, the median is the mean of the two middle values.
The mode is the most common value in a data set.
Dispersion is a measure of how spread out the data is. The range of a set of data is a measure of dispersion and is the difference between the largest and smallest values in a data set. The use of the word range in a statistical context is different than the use of the word range when working with functions, where range describes the possible outputs of a function.
Example 1
Determine the mean, median, mode, and range for the following set of data.
13, 14, 9, 17, 11, 9, 14, 9, 15, 12, 9, 14
Mean:
Median:
To determine the median, order the data values from smallest to largest and
identify the middle value.
9, 9, 9, 9, 11, 12, 13, 14, 14, 14, 15, 17
There are two middle values, so find the mean of the two values.
Mode:
The mode is 9 because it occurs more times than any other value.
Range: