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Filename: controllers/calculator.php

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Median calculator tool is used to find the median value which is exactly at middle in the given set of observations. For finding a median the observations are arranged in an increasing or decreasing order and the middle value is our median. If there is more than one single value in the middle then the median is an average of the middle numbers.

For a normal distribution, Mean = Median = Mode.

For an uniform distribution in the given interval say [x, y] the median is , which is equal to mean.

**Example 1: Find the median for the sample 45, 96, 2, 36, 25, 41, 12, 7, 3, 46, 21**

Number of numbers in the given sample = n = 11

Arranging the given sequence in increasing order:

2, 3, 7, 12, 21, 25, 36, 41, 45, 46, 96

Here n is odd so the median is given by the formula element

Median = = = 6^{th} element

Here the 6^{th} element is 25. Hence 25 is the median for the given data.

**Example 2: Find the median for the observations 32, 99, 25, 1, 34, 81, 27, 16, 64, 51, 19, 38**

Number of observations in the given sample = 12

Arranging the given sequence in increasing order:

1, 16, 19, 25, 27, 32, 34, 38, 51, 64, 81, 99

Here n is even. So the middle numbers are element and element

Middle numbers = element and element

Middle numbers = element and element

Here 6^{th} element = 32 and 7^{th} element = 34

Median is the mean or average of 6^{th} and 7^{th} element.

Median = = = 33