# How do I calculate the Mean, Mode and Median?

How do I calculate the Mean, Mode and Median?

Mean, mode and median are three types of measures of central tendency in statistics. While describing a set of data, the central position of any data set is identified. This is also known as the measure of central tendency. Now the question arises if we can extract some important features of the data by taking into account certain representatives of the data. This can be done by using the measures of central tendency or averages, namely mean, median and mode.

Let us study mean, mode and median in detail.

Mean, Median and Mode in Statistics

Mean, mode and median are the measures of central tendency which are used to study certain characteristics of a given set of data. A measure of central tendency talks about a set of data by showing the central position in the data set as a single value. One can imagine it as a tendency of data which gathers around a middle value. The three types of measures of central tendency which are most common are mean, mode and median.

Mean

The arithmetic mean of a given data can be defined as the sum of all observations divided by the number of observations. Let us suppose that a cricketer’s score in five ODI matches are as follows: 12, 34, 45, 50, 24. To take out his average score in a match, the arithmetic mean of data is calculated by using the mean formula:

Mean = (12 + 34 + 45 + 50 = 24)/5

Mean = 165/5 = 33

Mean is represented by (pronounced as x bar).

Types of data

Data can be shown in raw form or tabular form. Let us take out the mean in both cases.

Raw Data

Let us consider   to be n observations.

The arithmetic mean can be found out by using the mean formula

Frequency Distribution (Tabular) form

When the data is given in tabular form, the following formula is used:

Let us take out the following example

Example 1:Take out the mean of the following distribution:

Solution:

Below is the calculation table for arithmetic mean:

So, mean = 9

Median

The value of the middlemost observation which we get after arranging the data in ascending order is called as the median of the data.

For example, let us take the data 4,4,6,3,2 and arrange this data in ascending order: 2,3,4,4,6. Here are 5 observations. Therefore, median = middle value which is 4.

Case 1: Ungrouped Data

• Step 1: Let us arrange the data in ascending or descending order.
• Step 2: Let us take the total number of observations to be n.

To take out the median, we have to see whether n is even or odd. When n is odd, the following formula is used:

Median = (n + 1)/2th observation

Case 2: Grouped Data

When the data is continuous and in the form of a frequency distribution, then the median is taken out as shown below:

Step 1: Let us take out the median class.

Let n be the total number of observations i.e.

It is to be noted that median class is the where (n/2) is there.

Step 2: The following formula is used to find out the median.

Where,

• l = lower limit of median class
• c = cumulative frequency of the class which appears before modal class
• f = frequency of the median class
• h = size of the class

Mode

The value which occurs most frequently in the given data i.e., the observation with the highest frequency is known as the mode of data.

Case1: Ungrouped Data

For ungrouped data, the observation which appears maximum number of times is taken.

Mode = Observation with maximum frequency

Let us take the dta:6,8,9,3,4,6,7,6,3. Here, the value 6 occurs the maximum number of times. Therefore, mode = 6. There is an easy way to remember mode which is: Most Often Data Entered.

It is to be noted that a data may have no mode, 1 mode or more than 1 mode. According to the number of modes the data has, data can be unimodal, bimodal, trimodal, or multimodal.

Case 2: Grouped Data

When the data is found, the mode can be taken out by using the following steps:

• Step 1: Take out the modal class i.e., the class with maximum frequency.
• Step 2: Take out mode using the following formula:

Mode =

Where,

• l = lower limit of modal class
• = frequency of modal class
• = frequency of class which appears before modal class
• = frequency of class which appears after modal class
• h = size of class