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.

Step	Directions	Example
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

References

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

Cite this article as:

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.)
9/3/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/18/2009: Added "References". (McAdams, David E.)
6/7/2008: Corrected spelling. (McAdams, David E.)
3/17/2008: Initial version. (McAdams, David E.)