MEDIAN

Returns the median of a set of numbers.

Syntax:

MEDIAN(number1, number2, ... number30)

number1 to number30 are up to 30 numbers or ranges containing numbers.

MEDIAN returns the median (middle value) of the numbers. If the count of numbers is odd, this is the exact middle value. If the count of numbers is even, the average of the two middle values is returned.

Example:

MEDIAN(1, 5, 9, 20, 21)

returns 9, the number exactly in the middle.

MEDIAN(1, 5, 9, 20)

returns 7, which is the average of 5 and 9, the two numbers in the middle.

Application:

A small company wants to analyze the salary data of its employees to understand the central tendency of their income. They have the following salaries for their 9 employees:

	Employee ID	Monthly Salary
	A	B
1	101	$3,500.00
2	102	$4,200.00
3	103	$6,000.00
4	104	$3,800.00
5	105	$4,500.00
6	106	$9,000.00
7	107	$5,500.00
8	108	$4,100.00
9	109	$3,900.00

Goal: Find the median salary.

Step 1: Arrange the salaries in ascending order.

3,500, 3,800, 3,900, 4,100, 4,200, 4,500, 5,500, 6,000, 9,000

Step 2: Identify the middle number.

Since there are 9 salaries (an odd number), the middle number is the (9 + 1) / 2 = 5th value in the ordered list.

The 5th value is 4,200.

The MEDIAN function result:

MEDIAN(3500, 4200, 6000, 3800, 4500, 9000, 5500, 4100, 3900) = 4,200

Why is the Median useful here?

The mean (average) salary would be ($3500 + $3800 + $3900 + $4100 + $4200 + $4500 + $5500 + $6000 + $9000) / 9 = $4,944.44.

Notice that the average salary is pulled up by the single high outlier salary of $9,000. The median, however, is not affected by this extreme value. It gives a better representation of what a "typical" employee salary is in this company, making it a more robust measure of central tendency in this case.

Result of MEDIAN:

$4,200.00

Result of AVERAGE:

$4,944.44