Enter the set of numbers into the calculator to determine the range, median, and mode.

Range Median Mode Formula

The following formula is used to calculate the range, median, and mode of a set of numbers. 

Range = Max(X) - Min(X)

Median = Middle value of X when X is sorted in ascending order

Mode = Most frequently occurring value in XVariables:

  • Range is the difference between the highest and lowest values in the set (X)
  • Median is the middle value when the set (X) is sorted in ascending order
  • Mode is the most frequently occurring value in the set (X) X is the set of numbers

To calculate the range, subtract the smallest number in the set from the largest number. To calculate the median, sort the numbers in the set in ascending order and find the middle value. If there is an even number of values, the median is the average of the two middle numbers. To calculate the mode, find the number that appears most frequently in the set. If no number appears more than once, the set has no mode.

What is a Range Median Mode?

Range, median, and mode are statistical measures that describe a data set. The range is the difference between the highest and lowest values in the set. The median is the middle value when the data set is arranged in ascending or descending order. If the set has an even number of observations, the median is the average of the two middle numbers. The mode is the value that appears most frequently in the data set. A set may have one mode, more than one mode, or no mode at all.

How to Calculate Range Median Mode?

The following steps outline how to calculate the Range, Median, and Mode.

  1. First, determine the highest value (Max(X)) and the lowest value (Min(X)) in the set (X).
  2. Next, calculate the Range by subtracting the lowest value from the highest value: Range = Max(X) – Min(X).
  3. Sort the set (X) in ascending order.
  4. If the set (X) has an odd number of values, the Median is the middle value. If the set (X) has an even number of values, the Median is the average of the two middle values.
  5. To find the Mode, determine the value(s) that occur(s) most frequently in the set (X).

Example Problem:

Use the following set of numbers (X) as an example problem to test your knowledge:

X = {5, 2, 8, 4, 2, 9, 5, 8, 3}