Range is one of the measures of dispersion. It helps us understand how dispersed any dataset is. The range can be calculated using the highest and lowest observations of any dataset. However, while the range offers a simple indication of spread, it may be influenced by outliers, potentially skewing interpretations.

Additionally, in conjunction with other measures of dispersion, such as variance and standard deviation, a more comprehensive understanding of data variability can be obtained. In this article, we will discuss how to calculate the range for any dataset using the formula.

What is Range in Statistics?

The range, a measure of variability in statistics. It is the difference between the highest and lowest values in a dataset.

Range determines the spread of numbers or data from the lowest to the highest value. In mathematics, the range is the difference between the maximum and minimum values.

For example, if we have a dataset {2, 5, 8, 10, 3}, the range is calculated as 10 – 2 = 8. It represents the spread of observations and is obtained by subtracting the highest observation from the lowest. Range is the simplest and quickest way to understand the distribution of data points.

Range Formula

The formula of the range in statistics can be simply given by:

Range = Highest Value – Lowest Value

OR

Range = Highest Observation – Lowest Observation

OR

Range = Maximum Value – Minimum Value

How to Find Range in Statistics?

Here’s a step-by-step guide on how to find the range in statistics:

Step 1: Arrange the given values in ascending order. Start by writing down all the values from lowest to highest.

Step 2: Find the highest and lowest values from the dataset.

Step 3: Subtract the lowest value from the highest.

Let’s consider an example for better understanding.

Example: The number of hours spent by employees commuting to work in a week are: 30, 31, 35, 49, 45, 50. Determine the range of commuting hours.

Solution:

Given Dataset: 30, 31, 35, 49, 45, 50

Arrenging the data in ascending order as: 28, 31, 35, 45, 49, 50

Thus, Range = Maximum Value – Minimum Value

⇒ Range = 50 – 28 = 22

Hence, range of the given dataset is 22.

Read More,

• Range in Statistics
• Interquartile Range Formula
• Quartile Formula

Sample Questions on Calculate Range

Example 1: The number of goals scored by a football team in seven matches are: 2, 3, 1, 4, 2, 5,9. Determine the range of goals scored.

Solution:

Given Dataset: 2, 3, 1, 4, 2, 5,9

Arrenging the data in ascending order as: 1, 2, 2, 3, 4, 5, 9

Thus, Range = Maximum Value – Minimum Value

⇒ Range = 9 – 1 = 8

Hence the range of the goals scored in seven matches is 8.

Example 2: The diameters (in centimeters) of ten oranges are: 7, 8, 9, 10, 12, 8, 9, 11, 13, 10. What is the range of diameters?

Solution:

Given Dataset: 7, 8, 9, 10, 12, 8, 9, 11, 13, 10

Arrenging the data in ascending order as: 7, 8, 8, 9, 9, 10, 10, 11, 12, 13

Thus, Range = Maximum Value – Minimum Value

⇒ Range = 13 – 7 = 6

Hence range of the diameters will be 6.

Example 3:The distances (in kilometers) traveled by five cyclists are: 10, 15, 20, 15, 30. Determine the range of distances.

Solution:

Given Dataset: 10, 15, 20, 15, 30

Arrenging the data in ascending order as: 10, 15, 15, 20, 30

Thus, Range = Maximum Value – Minimum Value

⇒ Range = 30 – 10 = 20

Hence range of the distances will be 20.

Example 4: The ages (in months) of babies in a daycare center are: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. What is the range of ages?

Solution:

Given Dataset: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

Arrenging the data in ascending order as:6, 8, 10, 12, 14, 16, 18, 20, 22, 24

Thus, Range = Maximum Value – Minimum Value

⇒ Range = 24 – 6 = 18

Hence range of ages will be 18.

Practice Questions on Range

Question 1: Find the range of the following set of numbers {4, 6, 8, 10, 12}.

Question 2: In a math class, the test scores of six students are 85, 92, 78, 90, 88, 95. Determine the range of scores.

Question 3: The ages of children in a classroom are 6, 7, 6, 8, 9, 7, 6, 10, 11. What is the range of ages?

Question 4: The heights (in centimeters) of students in a class are as follows: 156, 162, 169, 155, 175, 180, 150, 172, 168, 178. What is the range of heights?

Question 5: A company has recorded the following profits (in thousands of dollars) over five years $200, $300, $250, $400, $600. Calculate the range of profits.

Question 6: The temperatures (in degrees Celsius) recorded over a week are 20, 22, 18, 25, 23, 21 and 24. What is the range of temperatures?

Question 7: The number of hours spent studying for a test by eight students is 4, 6, 3, 7, 5, 8, 2, 5. Determine the range of study hours.

FAQ’s on Range Calculation

What is a range in maths?

In statistics, the range of observations is the value obtained by subtracting the lowest value from the highest value in a dataset.

What is the basic formula of range?

Range (X) = Highest observation – Lowest observation

How to calculate range?

• Arrange the observations in ascending order.
• Subtract the lowest value from the highest .

Can the Range be a Negative Number?

No, the range cannot be negative because the range formula involves subtracting the lowest number from the highest number. Therefore, the range can only be zero or a positive number.

Can the range be zero?

Yes, the range can be zero if all values in the dataset are the same.