Range in Statistics

Table of Contents

• Range Meaning
• Range Formula
• Range of Ungrouped Data
• Range of Grouped Data
• How to Find the Range
• Solved Examples on Range
• Practice Problems
• Conclusion
• FAQs On Range

 

Range Meaning  

In statistics, the range is the simplest measure of how spread out the data is. It shows the difference between the largest and smallest values. The range helps us understand the variability of the dataset. Unlike the mean, median, and mode, it does not indicate where most of the data lies, but it gives a quick sense of how much the values differ.  

• Range = Highest value - Lowest value  

 

For instance, if the lowest score in a class is 10 and the highest score is 90, then the range is:  

Range = 90 - 10 = 80  

Thus, the range shows how far apart the largest and smallest numbers are in the dataset.  

 

Range Formula  

The standard Range formula  for range in statistics is:  

Range = Maximum value - Minimum value  

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

 

Range of Ungrouped Data  

Ungrouped data consists of raw numerical data that has not been sorted into groups or intervals.  

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

1. Arrange the data in ascending order (if needed).

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 is helpful for analyzing small sets of data without frequency distribution.  

 

Range of Grouped Data  

Grouped data organizes information into class intervals or frequency distribution tables.  

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

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

2. Find the lower boundary of the lowest class and the upper boundary of the highest class.

3. Apply the range formula:
   
   Range = Upper boundary of highest class - Lower boundary of lowest class

Example:

Upper boundary of the highest class = 40
Lower boundary of the lowest class = 10
Range = 40 - 10 = 30

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

 

How to Find the Range  

Here are the general steps to find the range:  

For Ungrouped Data:  

1.  List all the data values.  

2.  Identify the maximum and minimum values.  

3. Use the range formula: 
   
   Range = Maximum - Minimum  

 

For Grouped Data:  

1. Review the frequency table or class intervals.  

2. Identify the upper boundary of the highest class and the lower boundary of the lowest class.  

3. Use the range formula: 
   
   Range = Upper boundary - Lower boundary  

Knowing how to find the range is important for analyzing data, especially when comparing the spread of different datasets. 

 

Solved Examples on Range

Example 1 - Ungrouped Data:

Data: 8, 12, 15, 19, 23

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

This is a basic calculation of the range of ungrouped data.

 

Example 2 - Grouped Data:

Upper boundary of the highest class = 30
Lower boundary of the lowest class = 0
Range = 30 - 0 = 30

This is a standard example for calculating the range of grouped data.

 

Example 3 - Comparison with Measures of Central Tendency:

Data: 5, 7, 8, 9, 10, 30

• Mean = (5+7+8+9+10+30)/6 = 11.5

• Median = (8 + 9)/2 = 8.5

• Mode = No mode (all values appear once)

• Range = 30 - 5 = 25

This example shows how the range helps in measuring data spread, while mean, median, and mode provide information about central values.

 

Practice Problems

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. Calculate the range for the grouped data below:
   
   

This example shows how the range measures data spread, while the mean, median, and mode provide insight into central values.  

 

Conclusion  

The range in statistics is a basic yet powerful tool for measuring how data is spread. It is easy to calculate and helps to understand the variability of a dataset. By knowing the range of ungrouped and grouped data, and comparing them with the mean, median, and mode, one can get a complete view of how the data behaves. Learn how to find the range correctly and practice regularly with solved examples and practice problems to master this fundamental concept.

 

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Frequently Asked Questions on Range

1. What will be the range of the following data: 32, 41, 28, 54, 35, 26, 33, 23, 38, 40?

Ans: To calculate range:
Step 1: Identify the highest value = 54
Step 2: Identify the lowest value = 23
Step 3: Subtract lowest from highest:
Range = 54 - 23 = 31

 

2. How to calculate the range?

Ans: The range of a data set is calculated as:

• Range = Highest value - Lowest value

It shows how spread out the values in a data set are.

 

3. What is an example of a range?

Ans:
Example:
In the data set: 5, 10, 15, 20

• Highest value = 20

• Lowest value = 5

• Range = 20 - 5 = 15

 

4. What is called range?

Ans: Range is a measure of spread in statistics. It is the difference between the largest and smallest values in a data set. It tells us how widely the numbers are spread apart.

 

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