# Calculation of Mean, Median, and Mode

Mean, Median and Mode are the three statistical measures often used to encapsulate data sets. They are mainly known by the expected name “average”. There are many “averages” in statistics, but these three are the most common.

The “mean” is mainly the “average” where all the numbers are added up and then divided by the number of digits. The "median" is the "middle" value in the number series, and the "mode” is the value that occurs on numerous occasions. Out of these three measures, mode formula in statistics opens different ranges and aspects for the students

## Formulas of Mean and Median

The first theory to understand from mean, median and mode is mean. As described above, mean is the ratio of summation of all the values to the number of items. There are two types of Mean - simple arithmetic mean, and weighted arithmetic mean. If you want to know what is the formula of mean, go through the section given below:

Mean= ∑X ÷ N

[Here, ∑X = Sum of individual values and N = Total number of Items]

The simple arithmetic mean examines values in data as equal and permits equal importance to each value. On the other hand, in weighted arithmetic mean, weights or importance is assigned to the values.

To find the Median, the numbers should be arranged in numerical order from smallest to highest. Taking the number of observations as (n), and “th” signifies the (n)th number -

Median Formula = {(n+1)/2}th

Students who are looking for mean, median, mode formula pdf can wish to visit the official website of Vedantu.

## Mode Formula in Statistics for Discrete Series:

Mode comes third in the concept of mean, median and mode. As discussed earlier, it merely refers to the value that occurs most frequently in a number series. In discrete series, the values of items with their equivalent frequencies are found. Essentially, the value of the items with the highest frequency will be the mode for the distribution. Mode formulae in statistics help the students to solve different complicated statistical problems in their textbooks. Students can follow this method of mode in discrete series from an example shown below -

Example 1 - Find Mode from the following data

 12 14 16 18 26 16 20 16 11 12 16 15 20 24

Solution: Arranging data in ascending order

 11 12 12 14 15 16 16 16 16 18 20 20 24 26

The term that is occurring the maximum number of times is considered as Mode (Z). Here we get 16 four times, 12 and 20 two times each, and other terms once only. Thus Z=16

Students can find more examples of mode calculation in discrete series in Vedantu’s online classes.

## Illustrating Measures of Central Tendency

Mean, median, and mode are together known as measures of central tendency. It signifies synopsis of a data that represents the centre point or quintessential value of a dataset. These measures specify where most values in a distribution fall and are also referred to as the central location of a distribution. Best measures of central tendency can be chosen depending on the data you have. A “measure of central tendency” is either a location framework or a statistic used to evaluate a location parameter.

Several Measures of Central Tendency

• Arithmetic mean

• Median

• Mode

• Geometric mean

• Harmonic mean

• Generalized mean

• Weighted mean

• Truncated mean

• Interquartile mean

• Midrange

Students can solve their statistical problems with measures of central tendency formulas that are given below -

Arithmetic Mean (x̅) = ∑x/n

[Where ∑x is the summation of all the observations provided in a dataset and “n” is the number of observations]

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

## Mode Calculation for Continuous Series

While demonstrating the mode formula for continuous series, it is only one step forward of the method for discrete series. We get the value of Mode by interposing as in the case with a median. Mode formula in statistics is easy to understand and pretty simple to calculate Formula provided below has been used to calculate Mode (Z):

Mode (Z) = L+f1-f0/2f1-f0-f2 × i

Where L= lower limit of modal interval

f1= frequency correlating to modal interval

f2= frequency succeeding modal interval

i= length of modal interval

Several points while calculating mode -

• Class intervals must be absolute

• Length of the classes should be equal

• Series should be arranged in ascending order

• If the series is increasing, then convert it into continuous series

• If the first class is considered as a modal class, then f0 will be zero

• Similarly, if the last class is considered as a modal class, then fis zero

1. What is the Mean Value? Illustrate with a Numerical Example.

Ans. The most common form of “average” used is mean. To find mean value, we have to add up all the numbers and then divide by the number of data that you are equipped with.

For example, what is the mean of 2, 7, and 9? The solution is –

Adding the numbers: 2+7+9 = 18

No. of data = 3

Mean = 6

2. How Can We Calculate the Median in a Discrete Series?

Ans. To find out median in a discrete series, we need to follow a few steps -

(1) Firstly we have to arrange a given number series in an ascending or descending order

(2) Secondly, we need to calculate the increasing frequencies

(3) Thirdly, we need to use this formula to calculate median

Median= Size of (N+1)/2th item, where N (total of frequencies)

In the cumulative frequency, we need to search for the cumulative frequency that is equal to (N+1)/2 or the increasing frequency that is higher than this.

(4) The corresponding value of the variable is the value of the median.

3. What is the Mode Value?

Ans. Mode refers to the value that is frequently appearing in a set of values or number series. Note: If no number is often occurring in the series of items, then the answer will be "No mode." Students can find solutions based on mode formulas in statistics online.