Computing the Central Tendency of Data
To find the median, arrange all the scores from least to greatest, and find the score in the middle. We use "n" to indicate the number of elements in a data set. If "n" is odd, then the median is the term in the (n+1)/2 position. If "n" is even, then the median is the average of the terms in positions (n/2) and (n/2)+1.
Consider the observations {8, 25, 7, 5, 8, 3, 10, 12, 9} First, since we are working by hand, we might wish to arrange the data in order from least to greatest. {3, 5, 7, 8, 8, 9, 10, 12, 25} It then becomes easy to
- arrange the scores in order from smallest to largest (ascending order)
- count the number of scores (determine n)
- if n is an odd number, then the median = the (n+1)/2 term; In this case, n=9; therefore, the median is the (9+1)/2=5 or the fifth term, which is 8, just like the mode. NOTE: Don't confuse the position of the term with the value of the term. The median in this example isn't 5, it is the fifth term when arranged in ascending order, which is 8.
- if n is an even number, then the median is the average of the n/2 term and the term that follows it, the (n /2)+1 term.
- count the number of scores (determine n),
- determine the sum of the scores by adding them,
- divide the sum by n.
Again, in this case n = 9 and the sum = 87; therefore, the mean = 87 / 9 = 9.67
In this example, the n is still 9, the mode is still 8, the median is still 8, but the mean = 107/9 = 11.89
Extreme scores in a set of data have a more pronounced effect on the mean than on the median. Copyright 1997 © T. Lee Willoughby |