How to Find the Mean, Median, Mode, and Range of a Set of Numbers

Locate the landmarks in sets of numbers to discover similarities and disparities.
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Sets of numbers and collections of information can be analyzed to uncover trends and patterns. To find the mean, median, mode and range of any set of data is easily accomplished using simple addition and division.

Mean Means Average

Mean is the average amount within a set of numbers. To find the mean of how many goals a player makes in a soccer game, for example, first list the number of goals scored in each game, such as:

  • 3
  • 3
  • 6
  • 2
  • 1

Add these numbers together to find the sum -- in this case 15 -- and then divide the sum by the total number of values in that set, which would be 15 divided by 5. The mean in this data set is 3, so this player averaged three goals each game of the five games played.

Median in the Middle

The median is the middle value in a set of numbers. To find the median such as the dog at a pet show with the middle weight, first put the weight amounts of all the dogs in order from least to greatest. This list might look like 12, 16, 21, 24, 32, 37 and 42. Find the middle number in the list by counting in from each end. The median is the number in the middle. In this case, 24 is the median weight of the seven dogs in a pet show.

Most Often Equals Mode

Mode is the number within a set of data that occurs most often. Mode can be determined by making lists of each piece of information in a collection. For instance, to determine the winning vote among candidates for public office, list the names and how many times each name receives a vote. Once all names have been counted and compared, the longest list, representing the most votes, is the selected candidate or mode within the data set.

Range From Highest to Lowest

The difference between the greatest and least amounts in a set of numbers is the range.To establish the range, list numbers from least to greatest. For example, to find the range between the most expensive seat at a concert and the cheapest seat, arrange the costs of all the seating choices. Find the smallest number on the list, then find the greatest number. Subtract the least expensive from the most costly, and the resulting difference is the range. This might look like $45.00 - $8.00 = $37.00, so these concert seats have a $37 range from most costly to least expensive.


About the Author

Julie Alice Huson is a parent and an educator with a Master of Science in education. She has more than 25 years of teaching experience, and has written educational materials for Colonial Williamsburg. She has also worked in consultation with the California Department of Education. Huson received a Fulbright Distinguished Award in Teaching in 2011.

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