Range Formula 

The range formula determines the difference between the highest and the lowest values in a given set of numbers. The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples. 

What Is the Range Formula?

The range formula is mostly used in statistics to determine the range given in a particular data set. The formula helps in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the large range means higher variability whereas the small range means low variability. The range formula includes the other aspects of statistics such as mean, median, and mode. Hence, the formula to calculate the range is: 

R = Highest Value (H) - Lowest Value (L)

Range Formula

R = H - L 

Where, 

• R is the range
• H is the highest value
• L is the lowest value

How to Apply Range Formula? 

In order to calculate the range using the range formula, there are two mean steps to be followed: 

• Step 1: Place all the numbers from the lowest to the highest value in the data set 
• Step 2: By using the range formula, subtract the lowest value from the highest value picked from the data set

These steps can be followed for any type of number such as whole numbers or fractions. The range formula can also be used if the numbers in the data set are either positive or negative. 

Examples Using Range Formula 

Example 1: Emma took 5 tests in chemistry in one semester. Her test scores are 95, 71, 90, 85, 65. Calculate the range of her test scores by using the range formula. 

Solution: Given, 95, 71, 90, 85, 65

First, let us arrange the given set in order from the lowest to the highest value. 

65, 71, 85, 90, 95

The highest value from the data set = 95 

The lowest value from the data set = 65 

Using the range formula, let us put the values, 

R = H - L 

R = 95 - 65 

R = 30 

Therefore, the range of her test scores is 30. 

Example 2: Mona is looking at investing in some stocks, listed below is a list of four companies along with their stock price. By using the range formula, find the range difference among these stock prices that will help Mona in investing. 

Solution: From the data given in the table, let's arrange it in order from lowest to highest. 

105.21, 112.60, 150.87, 205.12

The highest value = 205.12

The lowest value = 105.21

Using the range formula, let us put the values, 

R = H - L 

R = 205.12 - 105.21 

R = 99.91

Therefore, the range in price is 99.91. 

Example 3: Galaxy art gallery conducted a painting competition, where around 10 people participated. Their ages are 45, 18, 20, 38, 57, 32. What is the age range of the participants? 

Solution: Given the ages - 45, 18, 20, 38, 57, 32

Let us arrange it in order from the lowest to the highest. 

18, 20, 32, 38, 45, 57 

The highest number = 57

The lowest number = 18 

Using the range formula, 

R = H - L 

R = 57 - 18 

R = 39 

Therefore, the age range of participants is 39.