Economics » Methods and Tools of Economic Analysis » Measures Of Central Tendency

Median

Median

The median is defined as an average which is the middle number when figures are arranged in order of magnitude. In an even distribution (i.e. the number of figures is an even number), the median is the average of the two (2) middle numbers. The median is therefore, the value of the middle number.

Examples:

a. Find the median of the following set of values: 2, 8, 11, 13, 15, 6, 9, 20, 7.
b. Find the median of the following numbers: 20, 8, 12, 8, 10, 14, 18, 5.

Solution:

a. Re-arranging in ascending order: 2, 6, 7, 8, 9, 11, 13, 15, 20
No. of figures = 9. Therefore, it is an odd distribution and the middle number is single.
⸫ Median = 9.

b. Re-arranging in ascending order: 5, 8, 8, 10, 12, 14, 18, 20
No. of figures = 8. Therefore, it is an even distribution and there are two middle numbers. So, the average of the middle numbers has to be taken.
⸫ Median \(= \cfrac{10 + 12}{2}\)
\(= \cfrac{22}{2}\)
\(= 11\).

Merits of Median

  1. Computation in finding the median is very easy.
  2. Median is not affected by extreme values (the minimum and maximum values in a data set).
  3. It is easy to understand.
  4. It does not involve serious calculations.

Demerits of Median

  1. It is difficult to find when a large number of values are involved.
  2. The re-arrangement of numbers is, sometimes, a difficult task.
  3. It tends to ignore extreme values (the minimum and maximum values in a data set).

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