Range in Statistics: Meaning, Formula and Examples

Range is a measure of how spread out the values in a data set are. It is calculated by subtracting the smallest value from the largest value.

It helps us understand the variation in a set of data. A small range indicates that the values are close to each other, while a large range indicates that the values are more widely spread.

For example, in the data set 4, 8, 12, and 20:

Range = Highest Value - Lowest Value

Range = 20 - 4 = 16

Therefore, the range of the data is 16.

Table of Contents

• What is Range
• Range Formula
• Range of Ungrouped Data
• Range of Grouped Data
• How to Find the Range
• Solved Examples on Range
• Practice Problems on Range
• Frequently Asked Questions On Range

What is Range

The range is a measure of spread in a data set. It is calculated by subtracting the smallest value from the largest value in the data set.

For example, in maths class test, 10 students scored: 45, 80, 90, 70, 65, 55, 89, 47, 30, 62.  

Range = 90 - 45 = 45  

This tells us that the scores are spread out over 45 marks.

How to Find the Range? 

To find the range, arrange the data in ascending order (from the smallest value to the largest value).

Use range formula: Range = Largest Value - Smallest Value

Example: The ages of 6 children are: 11, 8, 13, 10, 9, 12

Step 1: Arrange in ascending order - 8, 9, 10, 11, 12, 13
Step 2: Largest value = 13, Smallest value = 8
Step 3: Apply the formula: Range = 13 - 8 = 5

So, the range of ages is 5 years.

Range Formula  

The general formula is:

Range = Maximum value - Minimum value

Example:

Data: 3, 7, 9, 15

Range = 15 − 3 = 12

Note: This Range formula applies to both grouped and ungrouped data, though the calculation method differs slightly based on the data type.

Range of Data

The range of data is the difference between the maximum value and the minimum value in a data set.

Example:

Data Set: 10, 15, 18, 22, 30

Range = 30 − 10 = 20

Therefore, the range of the data is 20.

Range of Ungrouped Data  

The range of ungrouped data is the difference between the largest value and the smallest value in a data set. Ungrouped data refers to raw data that has not been organized into groups or intervals.

To calculate the range of ungrouped data, follow these steps:  

1. Arrange the data in ascending order (if the numbers are not arranged).

2. Identify the highest value and the lowest value in the dataset.

3. Apply the range formula:
   
   Range = Highest value - Lowest value

Example:  

Data: 4, 7, 15, 20, 10, 12  

Highest value = 20  

Lowest value = 4  

Range = 20 - 4 = 16  

The range of ungrouped data helps analyze small sets of data without frequency distribution.  

 

Range of Grouped Data

When a data set contains many values, the data is often organized into class intervals such as 0 - 10, 10 - 20, and 20 - 30. This type of data is called grouped data. Since the exact values are not available in grouped data, the range is calculated using the lowest and highest class boundaries.

For grouped data, the exact minimum and maximum values are unknown. Therefore, the range obtained is an estimated range.

Range Formula of Grouped Data = Upper Limit of Highest Class - Lower Limit of Lowest Class

To calculate the range of grouped data, use these steps:  

1. Identify the lowest class and the highest class from the frequency table.

2. Apply the range formula:

         Range = Upper Limit of Highest Class - Lower Limit of Lowest Class

Example:

Lowest class interval = 10 - 20
Highest class interval = 30 - 40
Lower limit of lowest class = 10
Upper limit of highest class = 40

Range = 40 - 10 = 30

The range of grouped data helps in summarizing large data sets and understanding their spread.

Solved Examples on Range

Example 1: Find the range of given observations: 8, 12, 15, 19, 23.

Solution: Arrange the data in ascending order.

8, 12, 15, 19, 23

Here, the lowest value = 8 and the highest value = 23.

Range = Highest Value - Lowest Value
= 23 - 8
= 15

Hence, the required range is 15.

Example 2: Find the range of the following grouped data.

Solution: The lowest class interval is 0 - 10 - Lower class limit = 0

The highest class interval is 20 - 30 - Upper class limit = 30

Range = Highest limit - Lowest limit
= 30 - 0
= 30

Hence, the required range is 30.

Example 3: Find the range of the following data set: 12, 18, 25, 30, 42, 50

Solution: The data is arranged in ascending order. Hence, identifying the highest and lowest value.

Highest value = 50

Lowest value = 12

Range = Highest Value - Lowest Value

Range = 50 - 12

Range = 38

The range of the data is 38.

Example 4: Find the range of the following grouped data.

Solution:

• The lowest class = 30 - 40 - Lower class limit = 30

• The highest class = 70 - 80 - Upper class limit = 80

Range (X) = Highest limit - Lowest limit
= 80 - 30
= 50

Hence, the required range is 50.

Practice Problems on Range

1. Find the range for the following ungrouped data: 3, 7, 10, 2, 9, 12

2. The class intervals and frequencies are given below. Find the range of grouped data:

3. A data set has a minimum value of 11 and a maximum value of 59. What is the range?

4. Given the data: 10, 15, 20, 25, 30
   What are the mean, median, mode, and range?

5. Find the range of the following data set: 12, 18, 15, 20, 10, 25
   
   
6. The marks scored by six students are: 45, 52, 48, 60, 55, 50
   Find the range of the marks.
   
   
7. Find the range of the following numbers: 8, 14, 11, 19, 5, 17, 10
   
   
8. The daily temperatures (in °C) recorded over a week are: 28, 31, 29, 33, 30, 27, 32

   Find the range of the temperatures.

9. A shop sold the following number of notebooks in six days:
   35, 42, 38, 50, 45, 40

   Find the range of the data.

10. Calculate the range for the grouped data below:
    
    

 

Frequently Asked Questions on Range

1. What do we mean by range in statistics?

Answer: Range is a measure of dispersion that shows the difference between the highest value and the lowest value in a data set.

Range = Highest Value - Lowest Value

It helps us understand how spread out the data is.

2. What is the formula of range?

Answer: The formula of range is:

Range = Highest Value - Lowest Value

To find the range, identify the largest and smallest values and subtract them.

3. What is the range of 2, 4, 6, 8, 10?

Answer: Highest value = 10

Lowest value = 2

Range = 10 - 2 = 8

The range is 8.

4. What is the range of 3, 7, 2, 4, 7, 5, 7, 1, 8, 8?

Answer: Highest value = 8

Lowest value = 1

Range = 8 - 1 = 7

The range is 7.

5. What is the range of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?

Answer: Highest value = 10

Lowest value = 1

Range = 10 - 1 = 9

The range is 9.

6. What is range in maths?

Answer: In maths, range refers to the difference between the highest and lowest values in a set of numbers. It is commonly used in statistics to measure the spread of data.

7. What is range in math statistics?

Answer: In statistics, range is the simplest measure of dispersion. It is calculated by subtracting the smallest value from the largest value in a data set.

8. What is the range formula for Class 7?

Answer: Students in Class 7 learn that:

Range = Highest Value - Lowest Value

This formula is used to find how spread out a set of numbers is.

9. What is the range formula for Class 8 and Class 9?

Answer: For Class 8 and Class 9 statistics, the range is calculated using:

Range = Maximum Value - Minimum Value

The concept helps students understand measures of dispersion and data analysis.

10. Why is range important in statistics?

Answer: Range helps us understand the spread of data. A small range indicates that the values are close together, while a large range indicates greater variation in the data set.

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