In statistics, mean, median, and mode are three different types of averages and used commonly to solve complex problems in real world. Mean is the average where you add all the number and divide the sum of numbers by count of numbers. Median is taken as the middle value of the list. To find the median, you need to write numbers from smaller to largest and then find the median. In case of mode, the most repeated number is output. In case, all numbers are unique in the list then there is no mode for the list.

Median is the middle value in a dataset when numbers are arranged in increasing order i.e. from smaller to larger. There are certain basic median formulas and steps to find the median of the list.

- First of all, arrange the numbers in perfect order i.e. smaller to largest.
- If the total number of the count in the list is odd then finding median is easy.
- In case, the total number of the count in the list is even then median would be average of two middle points on the list.

The median is good to use when data include exceptionally higher or lower values that are difficult to calculate without basic median formulas.

If the total number of numbers(n) is an odd number, then the formula is given below:

\[\large Median=\left(\frac{n+1}{n}\right)^{th}term\]

If the total number of the numbers(n) is an even number, then the formula is given below:

\[\large Median=\frac{\left(\frac{n}{2}\right)^{th}term+\left(\frac{n}{2}+1\right )^{th}term}{2}\]

The world ‘Mean’ could have multiple interpretations if you look outside of statistics. For a news channel, mean could be the daily temperature where higher and lower temperature is added and divided by two to calculate the final temperature.

In statistics, mean is the average. It is suitable to use mean for real-life problems when dataset contains values that are scattered evenly with no exceptional higher or lower values. It should not be used if you want to calculate the average of data on an ordinary scale.

\[\large \overline{x}=\frac{\sum x}{N}\]

**Where**,

**∑**, represents the summation

**X**, represents scores

**N**, represents number of scores.

The Mode is defined as the number that is most repeated in the list. In case, all numbers are unique in the list then there is no mode for the list. There are certain conditions where you cannot calculate mean and median but finding mode is possible. For example, if you want to check most issued book in the library then it can be simplified through mode expression quickly.

Given sequence: 19, 12, 9, 5, 8, 5, 25, 8

Total number of numbers in the sequence(N) = 8

**Mean**:

Total number of numbers in the sequence(N) = 8

\[\large \overline{x}=\frac{\sum x}{N}\]

= (19 + 12 + 9 + 5 + 8 + 5 + 25 + 8) / 8

= 11.375

To calculate the median, first we need to arrange the sequence in the ascending order

Ascending order: 5, 5, 8, 8, 9, 12, 19, 25

Total number of numbers in the sequence = 8 = even number

\[\large Median=\frac{\left(\frac{n}{2}\right)^{th}term+\left(\frac{n}{2}+1\right )^{th}term}{2}\]

\[\large Median=\frac{\left(\frac{8}{2}\right)^{th}term+\left(\frac{8}{2}+1\right )^{th}term}{2}\]

\[\large Median=\frac{\left(\frac{8}{2}\right)^{th}term+\left(\frac{8}{2}+1\right )^{th}term}{2}\]

\[\large Median=\frac{{4}^{th}term+{5}^{th}term}{2}\]

\[\large Median=\frac{8+9}{2}\]

\[\large Median=\frac{17}{2}\]

Median= 8.5

Mode = It is the most frequently occurring value.

= In the sequence, 5 repeated two times and 8 also repeated two times.

= Mode = 5, 8

No concept in mathematics is useful if it is not applied to the real-world problem and the same is true for mean median mode too. They are suitable for a plenty of real-life problems in different situations. You have to analyze the situation deeply to check where to use Mean, median, and mode and find the appropriate one for that particular situation.

Understanding mean median mode is necessary for students who want to pass competitive exams or wanted to enroll for science or engineering fields. The applications are just always endless but the only condition is having a deep understanding of concepts without any confusion.