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Everything you need to know about Median in statistics!

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Median is a statisticians’ term that signifies the middle value of the given list of data, whether that list is arranged ascendingly or descendingly.  It is also commonly called a measure of central tendency simply because, like the median, it is also found to be a type of average. The mode and mean are the other two types of central tendencies. Mode is the value in a given data set that is repeated most often. Mean is the sum of all observations divided by the number of observations. Similarly, the median is the number that lies halfway between the lowest value and the highest value.

To determine the median, the data should be organized, first, from least to greatest. In probability distributions, a median is a number that separates the upper half of the distribution, which may be a sample or a population. Different distributions have different medians. Median formulas differ depending on whether the data set contains even or odd numbers of observations. It is thus necessary to first recognize whether the data set contains odd or even numbers of values. Medians use only one or two values, so they’re not affected by extreme outliers or skewed distributions of scores. Means and modes, however, are affected by skewed distributions.

How Can You Calculate The Median?

  • In case of odd observations: When there are odd numbers of observations, the formula for calculating the median is: Median = [(n+1)/2]th term, n is the number of observations.
  • In case of even observations: A median formula for an even number of observations is: Median = [(n/2)th term + {(n/2)+1}th]/2where n is the number of observations.

Examples:

  • Find the Median of 20, 31 and 55

Ans- They can be sorted in ascending order as follows: 20,31,55. The middle number is 31, so the median is 31.

  • Find the median of the following: 12,4,52,70,60,21,86,93,42,36,76, 81,59,68,65

Ans: let’s arrange the series in ascending order

4,12,21,36,42,52,59,60,65,68,70,76,81,86,93

It consists of fifteen numbers. Our middle is number eight: The median value for this collection of numbers is 60.

What Steps Are Involved In The Calculation Of Median?

A median can be found easily, sometimes without requiring any calculations. The general steps of finding the median are as follows:

  • Arrange all the given data into ascending order i.e. From lowest to highest
  • If there are even or odd numbers of values in the dataset, determine the number of values
  • In light of the results of the previous step, we can consider two distinct scenarios for further analysis:
    • The median value is the central value that will be used to divide an odd number of values into halves if there is an odd number of values.
    • You can calculate the median of the dataset if there are even numbers of values in the dataset. Calculate the mean of the two central values to determine the median of your dataset if there are even numbers of values.

How Can Median Be Used To Group Data?

For instance, suppose you need to plan an activity in your classroom for which you need to divide the class into two groups. But, you cannot do so arbitrarily, as it would be unfair. To make sure the activity succeeds, you must first determine what factors will make a difference. Let’s say one of the factors that we choose is the height of the students. Let’s note each student’s height and arrange the data ascendingly as 152 cm, 158 cm, 160 cm, 162 cm, 189 cm, and 195 cm. According to the above data, the median height is 161 cm. The above data can be divided easily into two groups. One group would be composed of students above 161 cm in height, while the second group would consist of students below 161 cm in height.

Median is quite commonly used in statistics. You can learn more about it from Cuemath, your best online maths learning platform.

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