Mean Median Mode Formula
The mean median mode formula tells us about the mean, median, and mode of the given data. Mean, median, and mode are the measures of central tendency. Mean is also known as the arithmetic mean of the given data. Median is the middlemost value of the given grouped data if the data is grouped and arranged in ascending order. Mode is the value that appeared most in the data. In this section, we will learn about the mean median mode formula along with solved examples.
What are the Mean, Median, Mode Formulas?
The Mean, median, and mode formulas are explained below separately for the group of data.
The mean is the average of the numbers and is used to measure the central tendency of the data.
It can be also be defined as the sum of all observations to the total number of observations.
Formula to Calculate Mean
The mean formula of given observations can be expressed as,
\[\text {Mean} = \dfrac{\text{Sum of Observation}}{\text{Total Numbers of Observations}}\]
Formula to Calculate Median
The Median Formula of a given set of numbers, say having n observations, can be expressed as:
If n is odd:
Median = (n + 1)/2 ^{th }term
If n is even:
Median = \( \dfrac{ \frac{n}{2}^{\text{th}} \text{term} + (\frac{n}{2} + 1)^{\text{th}} \text{term}}{2}\)
Formula to Calculate Mode
Mode for grouped data is found using the following formula.
\(\begin{align}Mode = L + h\dfrac{(f_mf_1)}{(f_mf_1)(f_mf_2)}\end{align}\)
Where,
 '\(\begin{align}L\end{align}\)' is the lower limit of the modal class
 '\(\begin{align}h\end{align}\)' is the size of the class interval
 '\(\begin{align}f_m\end{align}\)' is the frequency of the modal class
 '\(\begin{align}f_1\end{align}\)' is the frequency of the class preceding the modal class
 '\(\begin{align}f_2\end{align}\)' is the frequency of the class succeeding the modal class

Example 1: \(\begin{align} Age\: of \:students = \left \{ {14,15,16,15,17,15,18} \right \}\end{align}\). Find the mode using the mean median mode formula.
Solution:
Since there is only one value repeating itself, it is a unimodal list.
\(\begin{align} Mode = \left \{ {15} \right \}\end{align}\)
Answer: Mode = 15

Example 2: The ages of the members of a community center have been listed below:{ 42, 38, 29, 36, 40, 33, 41}. Using between the mean median mode formula, calculate the median of the abovegiven data.
Solution:
To find the median of the given set.
Given:
Set of ages for different members: { 42, 38, 29, 36, 40, 33, 41}
Arranging the set in ascending order: { 29, 33, 36, 38, 40, 41, 42}
Number of observations, n = 7 (odd)
Using Median Formula,
Median = (7 + 1)/2 ^{th }term
= 4^{th }term
= 38
Answer: Median of the givenset = 36

Example 3: Find the mean of the first five natural even numbers, using the mean median mode formula.
Solution:
Given data is 2, 4, 6, 8,10.
Using Mean Formula,
\[\begin{align*}\text {Mean} &= \dfrac{2+4+6+8+10}{5} \\ &= \dfrac{30}{5} \\ &=6\end{align*}\]
Answer: 6 is the mean of the first five natural even numbers.