# Arithmetic Mean - Range

## Definition

Range: The difference between the highest and the lowest values in the data is called the range of the data.
∴ Range = Maximum value - Minimum value

## Notes

### Range:

• A range is the collection of values spread between the Maximum value and the Minimum value.
• In mathematical terms, a range is a difference between the Largest (maximum) value and the Shortest (minimum) value in a given dataset.
• Range defines the spread of values in any dataset.
• Steps to find range:
1. Arrange the data in ascending order
2. Find maximum and minimum value of given dataset.
3. Put the maximum and minimum value in the below formula to find the value of the range.
∴ Range = Maximum value - Minimum value.

## Example

Find range of following data: 1, 0, 2, 3, 2, 6, 8, 10, 12, 12, 13.

Arrange the following data in ascending order:
0, 1, 2, 2, 3, 6, 8, 10, 12, 12, 13.

Maximum number = 13 and Minimum number = 0

Range = Maximum number - Minimum number
Range = 13 - 0
Range = 13.

## Example

The ages in years of 10 teachers of a school are:
32, 41, 28, 54, 35, 26, 23, 33, 38, 40

(i) What is the age of the oldest teacher and that of the youngest teacher?(ii) What is the range of the ages of the teachers?

(i) Arranging the ages in ascending order, we get:
23, 26, 28, 32, 33, 35, 38, 40, 41, 54.
We find that the age of the oldest teacher is 54 years and the age of the youngest teacher is 23 years.

(ii) Range of the ages of the teachers = (54 – 23) years = 31 years

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