[Maths Class Notes] on Mean Median Mode Formula Pdf for Exam

Mean, Median, and Mode are the three of the most commonly used averages in statistics. These three can also be defined as the different measures of the centre of a numerical dataset. Identification of the central position of any data set while describing a set of data is known as the measure of central tendency. Every day we come across different kinds of data in newspapers, articles, in our bank statements, mobile, electricity bills, etc. Is it possible to figure out some important features of the data by considering only a few representatives of the data? Yes, This is possible by using measures of central tendency or averages, namely mean, median, and mode.

Mean

Mean is the arithmetic average of the given data set. Mean is calculated by adding the sum of values in a data set and dividing it by the number of observations in the data set. 

x = ∑x / N

Where,

The mean is classified into three. They are,

• Arithmetic Mean

• Geometric Mean

• Harmonic Mean

Median

It is the middle point of a set of observations when the numbers are in ascending or descending order. 

Median = [(n + 1) / 2]

Median = [(n / 2) + (n / 2 + 1)]/2

Mode

Mode is the most often occurring value in a data set. The difference between the highest and lowest values in a data set is called the range.

Mode = 1 + [(fₘ − f₁) / (2fₘ − f₁ − f₂)] × h

Where,

• l is the lesser limit of the class

• fₘ is the frequency possessed by the modal class

• f₁ is the frequency possessed by the class before the modal class

• f₂ is the frequency possessed by the class after the modal class

• h is the width of the class

Relationship Between Mean, Median and Mode

The Mean, Mode and Median are related as

2 Mean + Mode = 3 Median

For Example,

If, Mode = 65 and Median = 61.6, Mean= ?

In this case, where mode and median are given and mean should be found.

Use (2 Mean + Mode = 3 Median) formula

2 Mean = (3 × 61.6) – 65

2 Mean = 119.8

Mean = 119.8 / 2

Mean = 59.9