Median

The median of a given set of numbers is the central number (the number in the middle). To find the median, the set of numbers should either be arranged in ascending (smallest to largest) or descending (largest to smallest) order. If there is an even amount of numbers in a set, then the median is the average of the two central numbers.

Example:

Find the median of the following set of numbers.

(a)          122, 130, 128, 123, 126, 124, 127, 125, 129

(b)          401, 406, 403, 405, 402, 404

(a)  The numbers in ascending order:

122, 123, 124, 125, 126, 127, 128, 129, 130

The central number is, 126.

Therefore, the median = 126.

(b) The numbers in ascending order:

401, 402, 403, 404, 405, 406

The central numbers are, 403 and 404.

Therefore, the median

Note: The median divides a set into two equal sets, with the same amount of numbers below and above the median.

To find the median of ungrouped data, if the sum of the frequency (n) is an odd number, then the median is the observation, if the sum of the frequency (n) is an even number, then the median is the average of   observations.

Example:

Find the median of the data below.

The number of observations (employees), (n) = 100

Since 100 is an even number, the median is the average of observations.

That is, the average of

The next step is to insert a cumulative frequency column.

Identify which row 50 falls under in the cumulative frequency column, the salary amount in that row is the 50^th observation.

That is, the 50^th observation is, 6000.

Identify which row 51 falls under in the cumulative frequency column, the salary amount in that row is the 51^th observation.

That is, the 51^th observation is, 6500.

Therefore, the median