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How to find the mean, median and mode of a data set

The rule: mean uses every value, median uses order, mode uses frequency

The mean is the total divided by the number of values. The median is the middle value after sorting; with an even number of values, average the middle two. The mode is the value that occurs most often. A data set may have one mode, several modes, or no mode if no value occurs more often than the others.

Problem

Example 1. Six students watched $20, 13, 4, 8, 14, 8$ movies. Find the median and mean, rounding the mean to the nearest tenth. Example 2. The numbers of pets reported are $2, 3, 2, 3, 1, 0, 4, 4, 0, 0, 2, 4$ . Find every mode.

Answer

Movie data: median

10.5

, mean

11.2

to the nearest tenth. Pet data: modes

0

2

and

4

Checked by sorting both sets, recounting frequencies and recomputing the sum.

Step-by-step solution

Example 1: median and mean

Sort the six values first:

4, 8, 8, 13, 14, 20

There are an even number of values, so the median is the average of the third and fourth values:

median = \frac{8 + 13}{2} = 10.5

For the mean, add all six values and divide by $6$ :

mean = \frac{20 + 13 + 4 + 8 + 14 + 8}{6} = \frac{67}{6} = 11.166 \dots

Rounded to the nearest tenth, the mean is $11.2$ .

Example 2: more than one mode

Count each value:

0 : 3, 1 : 1, 2 : 3, 3 : 2, 4 : 3

The greatest frequency is $3$ , reached by three values. Therefore the data set has three modes:

0, 2, 4

How to check yourself

The mean must lie between the smallest and largest values. The median must come from the center of the sorted list. For the mode, never stop after finding the first frequent value - another value may tie it.

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