How to Calculate Range in Statistics?

Range measures the spread of a data set by subtracting its smallest value from its largest value. This page covers the range formula, calculation methods for raw and frequency data, coefficient of range, properties, range tricks and solved examples for quantitative aptitude.

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What Is Range?

Range is the difference between the largest and smallest observations in a data set. Its formula is Range = Maximum value − Minimum value.

First identify the maximum and minimum values, then subtract the minimum from the maximum. For the data 6, 11, 15, 19, and 24, the range is 24 − 6 = 18. Range is expressed in the same unit as the observations.

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Range, Variance and Standard Deviation

Learn how to calculate and interpret range, variance, and standard deviation as measures of dispersion in statistics, including the role of each measure in describing data spread.

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Range Formula & Tricks

Important Formulas

Range of raw data
Range = L − S

L is the largest observation and S is the smallest observation.

Coefficient of range
Coefficient of range = (L − S) ÷ (L + S)

This relative measure is generally used when the observations are positive and L + S is not zero.

Range after a constant is added
Range of (x + c) = Range of x

Adding or subtracting the same constant from every observation does not change the range.

Range after multiplication
Range of (kx) = |k| × Range of x

Multiplying every observation by k changes the range by the absolute value of k.

Quick Tricks

Find only the extremes

To calculate range, do not arrange or process every observation unnecessarily. Identify the maximum and minimum values directly.

Example: For 18, 5, 27, 12, and 9, range = 27 − 5 = 22.
Handle negative values carefully

The largest value may still be negative. Subtract the minimum value using its sign.

Example: For −12, −7, −3, and −9, range = (−3) − (−12) = 9.
Use transformation properties

A common value added to or subtracted from all observations leaves the range unchanged. A multiplication changes the range by the absolute multiplier.

Example: If the original range is 8, multiplying every value by −3 gives a new range of |−3| × 8 = 24.

Range Concepts

Range from Ungrouped Data

For ungrouped data, range equals the largest observation minus the smallest observation.

The observations do not need to be sorted if the maximum and minimum can be identified directly. The range is zero only when all observations have the same value.

Example: For 14, 22, 8, 17, and 11, the largest value is 22 and the smallest is 8. Therefore, range = 22 − 8 = 14.

Range from a Frequency Distribution

In a frequency distribution, range is found from the highest and lowest values or class limits represented in the distribution.

For a discrete frequency table, use the smallest and largest data values having non-zero frequency. For a continuous grouped table, the usual range based on class boundaries is upper boundary of the last class minus lower boundary of the first class.

Example: If the first and last classes are 10–19 and 40–49, their continuous class boundaries are 9.5 and 49.5. The range is 49.5 − 9.5 = 40.

Coefficient of Range

The coefficient of range is a unit-free relative measure calculated as (L − S) ÷ (L + S).

It compares the difference between the extreme values with their sum. For L = 30 and S = 10, the coefficient is (30 − 10) ÷ (30 + 10) = 20 ÷ 40 = 0.5.

Example: If the maximum value is 45 and the minimum value is 15, coefficient of range = (45 − 15) ÷ (45 + 15) = 30 ÷ 60 = 0.5.

Effect of Changes in Data

Adding the same number to every observation does not alter the range, while multiplying every observation by k changes the range to |k| times the original range.

If the original extremes are L and S, after adding c they become L + c and S + c, so their difference remains L − S. Multiplication by a negative number reverses the order of the extremes, which is why the absolute value of k is used.

Example: For data with range 12, adding 7 keeps the range 12. Multiplying every value by −2 makes the range 24.

Range and Missing Values

A missing observation can be determined from the range when the known extreme and the required extreme are identified.

If the maximum is M and the range is R, the minimum is M − R. If the minimum is m and the range is R, the maximum is m + R. The missing value must actually be an extreme for this calculation to apply.

Example: If the maximum value is 38 and the range is 17, the minimum value is 38 − 17 = 21.

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Practice Range Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Range Revision Points

Key formulas and rules for solving range questions.

  • Range = Maximum value − Minimum value.
  • Range has the same unit as the original data.
  • The range is zero when all observations are equal.
  • For grouped continuous data, use class boundaries when the question requires the actual continuous range.
  • Coefficient of range = (L − S) ÷ (L + S), usually for positive observations.
  • Adding or subtracting the same constant from every observation does not change the range.
  • Multiplying every observation by k changes the range by |k|.

Related Topic Explainers

Mean of Ungrouped Data → Empirical Relation Between Mean Median and Mode →

Range FAQs

What is the range formula?

Range = Maximum value − Minimum value. For example, the range of 4, 9, and 13 is 13 − 4 = 9.

What is the range of −8, −2, 3, and 6?

The maximum is 6 and the minimum is −8. Range = 6 − (−8) = 14.

What happens to the range if 5 is added to every observation?

The range remains unchanged because both the maximum and minimum increase by 5.

What is the range if every observation is multiplied by −4?

The new range is 4 times the original range. The negative sign reverses the order but does not make the range negative.

How is range found from a continuous grouped frequency table?

Subtract the lower class boundary of the first class from the upper class boundary of the last class. For classes 10–19 through 40–49, the range is 49.5 − 9.5 = 40.

What is the coefficient of range when the maximum is 50 and the minimum is 20?

Coefficient of range = (50 − 20) ÷ (50 + 20) = 30 ÷ 70 = 3/7.

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