# Midrange of a Data Set

The midrange of a data set is the value between the biggest value and the lowest value.

To find the midrange of a data set, just add the biggest value to the smallest value and then divide the sum by 2.

Since you are just looking for the highest and lowest values, it is not necessary to put the data set in increasing order.

Therefore, the formula to find the midrange is

Midrange
Highest value + Lowest value / 2

## A couple of examples showing how to find the midrange of a data set

The following list shows the ages of 8 college freshmen. Find the midrange of this data set.

17       18        16       20         18           16          22            19

The biggest value is 22 and the smallest value is 16.

Midrange
22 + 16 / 2

Midrange
38 / 2
= 19

The midrange is easy to compute. However, the midrange is rarely used since it is very sensitive to extreme values.

Suppose we make a small change in the data set above that shows the ages of 8 college freshmen.

Let us replace 19 with 70.

17       18        16       20         18           16          22            70

Midrange
70 + 16 / 2

Midrange
86 / 2
= 43

The midrange is 40.

As you can see, 70 is an outlier and it definitely influenced the midrange.

The midrange of 40 may give people the impression that the ages of those going to college tend to be 43.

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