Mean, Median, Mode definition

Statistics is a discipline of study that is concerned with numbers and numerical data because its precise definition is "the science of numbers." English's term for statistics is derived from Latin status, Italian statista, and German statistika. Shakespeare and Milton both used the term "statist" in their literature to refer to someone who is crucial to the functioning of the state. As a result, the topic began as a state science.

States used to gather information on things like the number of services provided, the volume of logistics, the wages of personnel, etc. In order to operate the administration methodically. The state's income-expenditure ratio was appropriately estimated with the aid of statistics. Since statistics played a significant role in the monarchs' decisions, they may be thought of as a collection of numerical data on a variety of topics that were important to the state.

Only the first and third senses are typically used. Data or statistics that are numerical values relating to any field, such as data on national income, population, or output, are referred to as numerology when used in the plural. However, when it is used singularly, it comes from the field of statistics, which studies the processes involved in gathering, presenting, analyzing, and interpreting data, or statistical procedures.

Mean

The average of the provided integers is the same as the arithmetic mean. It is a number that represents all of the other numbers in a group of numbers. Let's say we have a set of numbers and we need to get the mean of that set. To do this, all we need to do is add the numbers together and divide the result by the total of the numbers. We can determine the mean of this group of data from this. The mean of the set of numbers is thus determined using the provided approach.

How to find mean

Let's use an example to better grasp this:

In a family, there are two brothers. The heights of those two brothers vary. The elder brother is 150 cm tall, while the younger brother is 128 cm tall. Now, their parents are curious about the two brothers' typical heights. To do this, he must calculate the average height of the two brothers by averaging their heights.

= (128+150)/2

= 278/2

= 139 cm

We calculated their average height and mean height by adding their two heights together and dividing the result by two.

Those two brothers are therefore 139 cm tall on average. As we can see, the average height is bigger than the younger brother's height and smaller than the elder brother's height, falling in between the two.

Formula of mean

Mean= Sum of terms/Number of terms

As you can see from the formula, we need to add up all the numbers that are supplied to us, and we've also determined how many there are in total. The next step is to divide the sum of the numbers by each one separately. By doing this, we will obtain a number that is known as the number mean.

Median

The number that falls exactly in the middle of the provided numbers is the median, to put it in very simple terms. The difference between the larger and smaller portions of the group is determined by the number. It is sometimes referred to as the mean share of the specified population.

We need to arrange the numbers in various ways in order to determine the median. For instance, if we need to find the median of a set of integers, we must either write the numbers in ascending order or decreasing order. The middle number in this set of numbers is referred to as the median of these numbers when they are arranged in this fashion.

How to find median

Example 1. Find the median of the given data:

2, 5, 7, 9, 12 in descending order?

Resolution:

First sort the numbers in descending order.

how:

12, 9, 7, 5, 2 like this.

So the median is 7. This is in the middle of the numbers.

Formula of median

We must first determine the total number of numbers in order to apply the formula. We use the following formula if the number of observations is even:

Median = [(n/2)^th term + ((n/2) + 1)^th term]/2

The number of observations, or n, is used in the calculation above.

The formula above applies when there are even numbers of observations; however, when there are odd numbers of observations, we use alternative formulas.

Median = [(n + 1)/2]^th term

Mode

The value that appears most frequently in a dataset is referred to as the mode. In other terms, it is the value that appears in a set of observations the most frequently. Along with the mean and the median, the mode can be used to describe the center tendency of a dataset.

How to find mode

As we saw from the information about mode above, the mode is the number that occurs the most frequently among the group members.

Example:

From the numbers below, determine this group's mode:

4, 89, 65, 11, 54, 11, 90, 56

Answer: As you are aware, we must identify a number with the highest frequency in order to determine the group's mode. Such a number is quite simple to locate.

We can immediately notice that this group contains 11 such numbers that are occurring the most frequently. Therefore, 11 is the group's mode.