Mean, Median, Mode, Range Calculator

Take the following data set. $$\text{15 18 18 17 18 19 17 18 21 20 17 14 18 19 18}$$

Find the sum of the set

First off, find the total size of the data set, and the sum of the values added together. There are 15 data points in the set, which can be summed together to get a total of 267. For help summing the points in a data set, check out our sum tool: Summation Calculator.

Find the mean

To find the mean, divide the sum by the number of data points.$$\frac{267}{15}=17.8$$

Find the median

The median is the middlemost number in the data set. To find it, first arrange the set by size. $$\text{14 15 17 17 17 18 18 18 18 18 18 19 19 20 21}$$

1. Cross off the two outer values, then continue until there is only 1 or 2 values left.
2. If there is 1 value, that is the median.
3. If there are 2, average them to find the median (add them together and divide by 2).
4. Since this data set has 15 values there is only 1 value remaining when all the outer values are crossed off, 18.
5. So 18 is the median for this data set.

Find the mode & frequency

To find the mode, first find the element frequency. That's a list of how many times each element appears in the data set.$$\begin{array}{|cc|}\hline Data& Frequency\\ 14& 1\\ 15& 1\\ 17& 3\\ 18& 6\\ 19& 2\\ 20& 1\\ 21& 1\\ \hline\end{array}$$The most common number is the mode. In this case, the mode is 18, which appears more than any other data point. If there are multiple numbers that appear the most, then they are each the mode. If every number appears the same amount, there is no mode.

Find the midrange, minimum & maximum

To find the midrange, we first need to find the minimum and maximum of the data set. The minimum for this set is 14, and the maximum is 21. For help finding the minimum and maximum, check out our minimum & maximum tool. $$\text{Midrange }=\frac{14+21}{2}$$The midrange for this data set is 17.5.

Find the Range

The range is a similar value, representing how far away the highest and lowest data points are.$$21-14=7$$The range for this data set is 7.