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Measures of Central Tendency – Mode & Median

The mode in statistics is the value that takes place the most commonly in a particular set. The value or number in a data set that has a high frequency or appears more frequently is also known as the mode or modal value. Aside from the mean and median, it is one of three measures of central tendency. The mode of the set 3, 7, 8, 8, 9, for example, is 8. As a result, we can easily find the mode for a finite number of observations. A set of values can have one mode, multiple modes, or no mode at all.

In this article, you will learn the definition of mode in statistics, the formula for mode for grouped data, and how to find the mode for the given data, i.e. for ungrouped and grouped data, as well as detailed solved examples.

What is the Median Formula?

The median of a set of data is the number in the middle or the center of the set. The median is also the halfway point in the set.

To find the median, arrange the data first in order of least to greatest or greatest to least value. A median is a number that divides a data sample, population, or probability distribution into upper and lower halves. Depending on the type of distribution, the median differs. In this article, we will discuss the median formula.

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

To find the median, first arrange the numbers in ascending order from smallest to largest. Then look for the number in the middle.

Median of Two Numbers

If a data set contains only two numbers, their median and mean will be the same (or arithmetic mean or average). For instance, the mean and median of 6 and 14 are both equal to 10.

Median of Three Numbers

If there are three numbers in a data set, arrange them in ascending or descending order first. The middle number is now the median of the given data set. For example, 17, 21, and 11 are three data set numbers. The numbers are now arranged in descending order: 21, 17, 11. As a result, 17 is the median.

Properties of Median

The properties of the median are explained in statistics in the following points.

  • The median is not affected by all of the data values in a dataset.
  • Individual values do not reflect the median value, which is determined by its position.
  • The distance between the median and the remaining values is less than the distance between any other point.
  • For each array, there is only one median.
  • Algebraically, the median cannot be manipulated. It is not possible to weigh or combine it.
  • The median is stable in a grouping procedure.
  • The median does not apply to qualitative data.
  • For computation, the values must be grouped and ordered.
  • The median of a ratio, interval, or ordinal scale can be calculated.
  • Outliers and skewed data have a smaller influence on the median.
  • When a distribution is skewed, the median is a better measure than the mean.

How Do You Find the Median?

To find the median, arrange all of the numbers in ascending order and look for the middle.

Example 1: Determine the median of 14, 63, and 55.

Solution:

In ascending order, they are: 14, 55, 63.

The median is 55, which is the middle number.

Example 2: Determine the mean of the following:

4, 17, 77, 25, 22, 23, 92, 82, 40, 24, 13, 12, 67, 23, 29

Solution:

When we arrange those numbers, we get:

4, 12, 13, 17, 22, 23, 23, 24, 25, 29, 40, 67, 77, 82, 92,

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

This set of numbers has a median value of 24.

To understand the topic in an interesting way, you can visit Cuemath.

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