# Median (Statistics)

Pronunciation: /ˈmi.di.ən/ Explain

The median of a data set is the middle value of the data set. For a data set with an odd number of members, it is the member of the data set with just as many values less than its value as greater than it. For a data set with an even number of members, it is the average of the two middle values of the data set. The median is used in statistics to analyze a data set.

StepDirectionsExample
For data sets with an odd number of members
Starting data set { 1, 8, 4, 3, 9, 3, 6, 4, 7, 5, 2 }
1 To find the median of a data set, first order all the members of the data set from lowest to highest. { 1, 2, 3, 3, 4, 4, 5, 6, 7, 8, 9 }
2 Count the number of members in the data set. There are 11 members of the data set.
3 Divide the number of members by 2 and round down. 11 / 2 = 5.5 ≈ 5
4 There are five members before the median and five members after the median. Count the members from the ordered data set. The median is the member after the fifth member. { 1, 2, 3, 3, 4, 4, 5, 6, 7, 8, 9 }
For data sets with an even number of members
Starting data set { 1, 8, 4, 3, 9, 3, 6, 7, 5, 2 }
1 To find the median of a data set, first order all the members of the data set from lowest to highest. { 1, 2, 3, 3, 4, 5, 6, 7, 8, 9 }
2 Count the number of members of the data set. There are 10 members of the data set.
3 Divide the number of members of the data set by 2. 10 / 2 = 5.
4 Calculate the average of the 5th and 6th members of the data set. 4 + 5 = 9. 9 / 2 = 4.5
1. McAdams, David E.. All Math Words Dictionary, median. 2nd Classroom edition 20150108-4799968. pg 115. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. median. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 9/2/2018. http://www.merriam-webster.com/dictionary/median. Buy the book

McAdams, David E. Median (Statistics). 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/median_statistics.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)