 # Median

In Statistics, to represent the typical value of the data set or the centre point, the three different measures of central tendencies are used. The measures of central tendency are mean, median and mode. The mean defines the average value of the dataset. The median represents the middle value of the data set. The mode represents the repeated value in the dataset. In this article, we are going to discuss the definition of median, and the procedure to calculate the median with examples are given in detail.

## What is the Median?

The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest. A median is a number that is separated by the higher half of a data sample, a population or a probability distribution, from the lower half. For example, the median of 3, 3, 5, 9, 11 is 5. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values: so the median of 3, 5, 7, 9 is (5+7)/2 = 6.

## Median Formula

The formula to calculate the median of the data set is given as follows:

If the total number of observation given is odd, then the formula to calculate the median is:

Median = {(n+1)/2}thterm

If the total number of observation is even, then the median formula is:

Median  = [(n/2)th term + {(n/2)+1}th]/2

### How to Calculate the Median?

To find the median, place all the numbers in the ascending order and find the middle.

Example 1:

Find the Median of 14, 63 and 55

solution:

Put them in ascending order: 14, 55, 63

The middle number is 55, so the median is 55.

Example 2:

Find the median of the following:

4, 17, 77, 25, 22, 23, 92, 82, 40, 24, 14, 12, 67, 23, 29

Solution:

When we put those numbers in the order we have:

4, 12, 14, 17, 22, 23, 23, 24, 25, 29, 40, 67, 77, 82, 92,

There are fifteen numbers. Our middle is the eighth number:

The median value of this set of numbers is 24.

Example 3:

Rahul’s family drove through 7 states on summer vacation. The prices of Gasoline differ from state to state. Calculate the median of gasoline cost.

1.79, 1.61, 2.09, 1.84, 1.96, 2.11, 1.75

Solution:

By organizing the data from smallest to greatest, we get:

1.61, 1.75, 1.79, 1.84 , 1.96, 2.09, 2.11

Hence, the median of the gasoline cost is 1.84. There are three states with greater gasoline costs and 3 with smaller prices.

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