Median
The median is the score of the scale that separates the upper half of the distribution from the lower, that is to say, it divides the series of data into two equal parts.
The median is denoted by M_{e}_{.}
The median can only be found for quantitative variables.
Calculation of the Median
1 Order the data from smallest to largest.
2 If the series has an odd number of measures, the median is the middle of the same score.
2, 3, 4, 4, 5, 5, 5, 6, 6Me = 5
3 If the series has an even number of scores the median is the average between the two central scores.
7, 8, 9, 10, 11, 12Me= 9.5
Calculation of the Median for Grouped Data
The median is in the class where the cumulative frequency reaches half the sum of the absolute frequencies.
That is to say, the median is within the class .
L_{i} is the lower limit of the median class.
is half the sum of the absolute frequency.
F_{i-1} is the absolute frequency immediately below the median class.
a_{i} is the width of the class containing the median class.
The median is independent of the widths of the classes.
Example
Calculate the median of a statistical distribution given by the following table:
f_{i} | F_{i} | |
---|---|---|
[60, 63) | 5 | 5 |
[63, 66) | 18 | 23 |
[66, 69) | 42 | 65 |
[69, 72) | 27 | 92 |
[72, 75) | 8 | 100 |
100 |
100/2 = 50
Median class: [66, 69)