There are various branches of mathematics. One of them is statistics. It is considered to be one of the significant branches of mathematics which deal with the study of collecting, analyzing, interpreting, and observing data. You may find various interesting topics related to statistics such as central tendencies, descriptive and inferential statistics, graphical representation, and many more. Statistics has a wide range of applications: sectors like sociology, probability, geology, and many more are closely related to statistics. In this article, we may cover some topics related to statistics such as standard deviation, types of central tendencies (mean, median, and mode).

What Do You Mean by Standard Deviation?
The term 'standard deviation’ can be defined as the positive root (square) of a particular variance. It is also considered to be one of the basic methods to approach statistical analysis. The standard deviationis abbreviated as ‘SD’ (s - standard and d - deviation). It is symbolized by the help of σ. The value of standard deviation is very closely related to the value of the mean. For instance, if the value of standard deviation is low, it means that the value of mean is close to that of standard deviation. The same goes for the higher value of SD.

Mean
Mean can be defined as the average value or mean value for a given set of frequencies or numbers. It is generally used to find the average marks of a student, or mean score scored by a cricketer and so on. The mathematical formula given is the sum of all the frequencies/total number of observations. Let us try to solve some examples related to the mean formula so that no doubts are leftover.

Example: Calculate the mean of the first five even numbers?

Solution: Given that,
First five even numbers = 2, 4, 6, 8, 10.
To find mean, formula = sum of all the frequencies / total number of observations.
2 + 4 + 6 + 8 + 10 / 5 = 30 / 5
30 / 5 = 6.
Therefore, the mean of the first five even numbers is equivalent to 6.

Median
Median is one of the types of central tendency which is considered as the middlemost or midpoint of a given observation. The mathematical formula is categorized into two types: formula for grouped and ungrouped data. The formula for odd or grouped data is n + 1 /2 th observation, where n is the number of observations. An example related to the median formula is mentioned below:

Example: Find the median of the first seven odd numbers?

Solution: According to the question,
First seven odd numbers = 1, 3, 5, 7, 9, 11, 13. (arranged in ascending order).
Using the formula for an odd set of numbers = n + 1 /2 th observation.
N = 7.
So, 7 + 1 / 2 = 8 / 2 th term.
8 / 2 th term = 4th term.
4th term = 7.
Hence, the median of the first seven odd numbers is equivalent to 7.
Mode

Mode is the last and the easiest central measure of tendency. It is defined as the value of a given data that has occurred most of the time. For example, if the number 11 has occurred 3 times comparatively more than any other frequency, then the mode is 11. There are three types of lists: monomial, binomial and trinomial lists. This depends on the number of modes for a given observation.

Example: Find the mode of the given data: 3, 5, 3, 9, 10, 7?
Solution: According to the question,
Given data = 3, 5, 3, 9, 10, 7.
Arranged in ascending order = 3, 3, 5, 7, 9, 10.
We can see that the number ‘2’ is occurring most of the time i.e. 2.
Thus, the mode of the given observation is equivalent to 2.

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