# Finding the Mode and Range of a Data Set

Range is a measure of variance of the data. The measure of centre gives an average value of the data set while the range gives a measure of how far the data is spread out.

## Rules to find the range of a data set

We look at the numbers of the data set and find the smallest and the largest numbers among them.

The difference between the largest number and the smallest number gives the range of the data.

Find the mode and range of the set of numbers given below −

14, 29, 14, 36, 78

### Solution

**Step 1:**

The number that repeats most is 14; So Mode = 14.

**Step 2:**

Range = greatest number – smallest number

= 78 – 14 = 64.

**Step 3:**

Mode = 14; Range = 64.

Find the mode and range of the set of numbers given below −

22, 59, 53, 85, 53, 34, 17

### Solution

**Step 1:**

The number that repeats most is 53; So Mode = 53.

**Step 2:**

Range = greatest number – smallest number

= 85 – 17 = 68.

**Step 3:**

Mode = 53; Range = 68.