http://www.ck12.org Chapter 6. Measures of Central Tendency - Basic
6.2 The Median
Learning Objectives
- Understand the median of a set of numerical data.
- Compute the median of a given set of data.
- Understand the mean of a set of data as it applies to real world situations.
Introduction
Young players from the minor hockey league have decided to order team wind suits. They must have their measure-
ments taken to ensure a proper fit. The waist measurement for each of the boys was taken and following are the
results:
Andy –27in. Barry –27in. Juan –23in. Miguel –27.5 in. Nick –28in.
Robert –22in. Sheldon –24in. Trevor –25in. Walter –26.5in.
What is themedianof these waist measurements?
You will be able to answer this question once you understand what is meant by themedianof the waist measurements.
The test scores for five students were 31, 62, 66, 71 and 73. The mean mark is 60.6 which is lower than all but one
of the student’s marks. The mean has been lowered by the one very low mark. A better measure of the average
performance of the five students would be the middle mark of 66. The median is the middle number, that number
for which there are as many above it as below it in a set of organized data. Organized data is simply the numbers
arranged from smallest to largest or from largest to smallest. The median, for an odd number of data, is the value
that divides the data into two halves. Ifnrepresents the number of data andnis an odd number, then the median will
be found in positionn+ 21.
Ifnrepresents the number of data andnis even, then the median will be the mean of the two values found before
and after then+ 21 position.
Example 1:Find the median of:
a) 10, 2, 14, 6, 8, 12, 4
b) 3, 9, 2, 5, 7, 1, 6, 4, 2, 5
Solution:
a) The first stem is to organize the data –arrange the numbers from smallest to largest.
10 , 2 , 14 , 6 , 8 , 12 , 4 → 2 , 4 , 6 , 8 , 10 , 12 , 14
The number of data is an odd number so the median will be found in then+ 21 position.
n+ 1
2=
7 + 1
2
=
8
2
= 4
The median is the value that is found in the 4thposition.