Median Calculator - CalcuNation

The median is the center number in a set of numerically arranged numbers. That only works if there is an odd amount of numbers in the set. It's a little different if there is an even amount of numbers in the set. The median is the mean average of the center two numbers once the group is arranged from low, to high.

The median tells you where the middle of a data set is. It’s used for many real-life situations. People in human resources will calculate the median salary in certain fields. Doing this helps them know what the typical “middle” salary is for a particular position.

The median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.

To calculate the median, first order the numbers from smallest to largest. Then find the middle number. For example, the middle for this set of numbers is 6, because 6 is right in the middle.
2, 2, 3, 3, 6, 7, 8, 9, 10.
You get the same result with the formula. There are 9 numbers in the set, so n = 9.

• {(9 + 1) ÷ 2}th
• = {(10) ÷ 2}th
• = {5}th

The 5th number in 2, 2, 3, 3, 6, 7, 8, 9, 10 is 6.

Keep in mind when using the median formula, the steps are different if you have an even or odd amount of numbers in your data set.

Find the median for an even set of numbers

Find the median for the following data set.
104, 57, 35, 99, 90, 102, 11, 55.

Step 1: Place the data in ascending order (smallest to highest).
11, 35, 55, 57, 90, 99, 102, 104.

Step 2: Find the TWO numbers in the middle (there should be an equal amount of numbers above, and below, the two numbers).
11, 35, 55, 57, 90, 99, 102, 104

Step 3: Add the two middle numbers and then divide by two, to get the average:

• 57 + 90 = 147
• 147 / 2 = 73.5.

The median is 73.5.

Median Average vs. Mean Average

Real estate agents will sometimes use the median price of houses to gain a better idea of the typical home price for a set area. This is useful because the median doesn't change much based on outliers that might be in a data set. If you live in a neighborhood with many homes in the $150k to $200k range, one multi-million dollar home would throw off an average of what a consumer could expect, if mean average is used, compared to the median.