Definition:
Definition:
The median, is the score value which cuts the distribution in half, such that half the scores fall above the median and half fall below it.
Illustration :
The first step is to rank order the scores from lowest to highest. The procedure branches at the next step: one way if there are an odd number of scores in the sample distribution, another if there are an even number of scores.
If there is an odd number of scores as in the distribution below:
32 32 35 36 36 37 38 38 39 39 39 40 40 45 46 then the median is simply the middle number. In the case above the median would be the number 38, because there are 15 scores all together with 7 scores smaller and 7 larger.
If there is an even number of scores, as in the distribution below:
32 35 36 36 37 38 38 39 39 39 40 40 42 45 then the median is the midpoint between the two middle scores: in this case the value 38.5. It was found by adding the two middle scores together and dividing by two (38 + 39)/2 = 38.5. If the two middle scores are the same value then the median is that value.
In the above system, no account is paid to whether there is a duplication of scores around the median. In some systems a slight correction is performed to correct for grouped data, but since the correction is slight and the data is generally not grouped for computation in calculators or computers, it is not presented here.
Application:
Applet :
Check the following applet for an illustration of the median and mean http://www.ruf.rice.edu/~lane/stat_sim/descriptive/
The Jameson family drove through 7 states on their summer vacation. The price per gallon of gasoline varied from state to state. What was the median gasoline price paid?
$1.79, $1.61, $1.96, $2.09, $1.84, $1,75, $2.11
(Solution)
During the first marking period, Nicole had math quiz scores of 90, 92, 93, 88, 95, 88, 97, 87, and 98. What was the median of her quiz scores?
(Solution)
A marathon race was completed by 4 participants. What was the median time given in hours below?
2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr
(Solution)
The salaries of 8 employees at a small company are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000
(Solution)
Find the mean for the following data using Excel:
mean.xls
Comments :
The median is not effected by extreme scores, as the following distribution of scores indicates:
32 35 36 36 37 38 38 39 39 39 40 40 42 55 The median is still the value of 38.5. The median is not as quick and dirty as the mode, but generally it is not the preferred measure of central tendency.
For a comparison between mean and median - http://standards.nctm.org/document/eexamples/chap6/6.6/
Additional exercise:
For the excel worksheet provided in the above example, find the mean and the mode.