How To Find the Range of a Set of Data in Maths

How to Find Range

In statistics, we find the range of a set of data by subtracting the lowest value of the data set from the highest value of the data set.

Why is the Range Important you may ask! Finding the Range in a set of data is a great way to get a primary understanding of how spread-out or variable a set of data really are.

Range is also the quickest and easiest way to measure variation.

Question

A group of 10 students were shown their test scores; 21 25 20 16 19 28 30 29 15 22. What is the range of the test scores?

Step 1: List the Components of the Data Set

How to find Range

When you want to find the range of a set of data, you’ll need to list all of the components of the data set so that you can easily spot the highest and lowest numbers.

It’s best practice to write the numbers down in ascending order, which means, you need to write the numbers down from the lowest to the highest. in this example, that will be; 15,16,19,20,21,22,25,28,29,30.

Step 2: Identify the Lowest and The Highest Numbers in The Data Set

In this step of find the range of a set of data, you need to identify the lowest/minimum number and the highest/maximum number in the data set.

In this scenario, the lowest number in the set of data is 15 and the highest number is 30.

Step 3: Subtract the Lowest From the Highest Number in Your Set of Data

Once you have identified the lowest and the highest numbers in your set of data, you’ll need to subtract the lowest number in your set of data from the largest number to find the ‘Range’. i.e (Range; 30 – 15 = 15). Range = 15.

How to Calculate/Find the Range Using Excel

The video above will explain all you need to know about finding the range using excel.

Knowing how to calculate the range of a set of data in Excel is a very important skill for any business, as you may need to find out information such as the highest and lowest values of sales, revenues, or any other information which is recorded on Excel spreadsheet.

It’ll be too tedious to sort through rows and rows of Excel spreadsheets trying to find the difference between the lowest and highest value of a given set of data. Knowing the range can help make valuable business decisions.

Finding the range in Excel is quite easy and straightforward. You can find the range by using the MAX and MIN functions in Excel

find range using excel

Using the data in the Excel spreadsheet above we can easily calculate the range of the given set of data.

The formula to find the range in Excel wil be =MAX(B2:B11)-MIN(B2:B11)

To find the Maximum value of the set of data in Excel, in cell B14 type =MAX(B2:B11)

To find the Minimum value of the set of data in Excel, in cell B15 type =MIN(B2:B11)

Now you can easily see the minimum and maximum value in your data. To find the Range simple type in cell 16 ( =B14-B15). This formula will work out the range of the set of data.

How to Find Interquartile Range of a Set of Data

What does interquartile range mean

The interquartile range is simply a measure used to describe the middle 50% of a given set of data when ordered from the lowest to the highest value.

Furthermore, the interquartile range is used to measure where the bulk of the value of a set of data lies.

This therefore makes it the preferred method for measuring spread especially for data such as school performances.

Steps for Finding Interquartile Range

To find the interquartile range, we need to ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3).

The interquartile range is simply the difference between Q3 and Q1.  

  •   Sort your data in ascending order. i.e from the lowest to the highest.

15,16,19,20,21,22,25,28,29,30,35.

  •  Find the median

15,16,19,20,21,22,25,28,29,30,35.

  • Place enclosures around the numbers before and after the median to easily identify the numbers.

(15,16,19,20,21),22,(25,28,29,30,35).

  •      Calculate the median of both the lower and upper half of the data. Where Q1 is the median for the lower half of the data and Q3 is the median for the upper half.

(15,16,19,20,21),22,(25,28,29,30,35).

Q1 = 19 , Q3 = 29

  •      The interquartile range is the difference between the upper and lower medians i.e IQR = 29 – 19 = 10
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