There are several other useful measures than mean, median, or mode to support you with analyzing a data set.

As you look at a data set, often, you may want to comprehend the data spread or the gap between the least and the greatest number.

Now, this the data range, and to find that range, we subtract the data set’s least value from its greatest value.

To give you an example, if the data set consists of \(2,\,3, \,5, \,4, \,5,\,\) and \(5,\) the set’s least value is the \(2\), and the set’s greatest value is the \(5\). So the set’s range is \(5\) minus \(2\), which is \(3\).

It may also be useful to know which number or value is mid-way between the data set’s least value and greatest value. This value or number is what we call the midrange.

To discover that midrange, we have to add the greatest and the least values together and divide that number by \(2\). Or, to use other words, discover the mean of the set’s greatest and least values.

In the data set \(2, \,5,\, 3,\, 4,\, 5,\,\)and \(5\), the midrange is: \(\frac{2+5}{2}=\frac{7}{2}=3.5\)

Let’s take a look at some other examples.

**Example One**

Problem: Discover the midrange and range for the following number set: \(2, \,7,\,4, \,10, \,35,\, 14\,\).

The range is \(35 – 2\), which is \(33\). To discover the range, subtract the number set’s least value from the set’s greatest value.

The midrange is: \(\frac{35+2}{2}=\frac{37}{2}=18.5\)

Add the set’s greatest and least values together and divide that number by two.

**The Answer is:**

Range: \(33\)

Midrange: \(18.5\)

**Example Two**

Problem: Discover the midrange and range for this number set: \(62, \,20,\, 88, \,145, \,105, \,37, \,93,\,\) and \(22\).

The least number is \(20\) As this data set is in the order least to greatest, first find the least and the greatest number.

The greatest number is \(145\)

The range is \(145\) minus \(20\), which is \(125\). Subtract the set’s least value from the set’s greatest value to discover the range.

The midrange: \(\frac{145+20}{2}=\frac{165}{2}=82.5\)

Now, we add the least and the greatest values together and divide that number by two.

**The Answer is:**

Range: \(125\)

Midrange: \(82.5\)

Next lesson: Perimeter and Area

*Last Updated on April 12, 2021.*