Mean

Measures of Central Tendency recognize a central or middle position within a collection of data. They are also classified as summary statistics. It is an approach to analyzing and predicting different types of information in real-world situations in the form of tables and graphs. It is a statistical model that represents a singular value of the database provided. It provides an accurate description of particular data. The most commonly used measures of central tendency are the mean, median, and mode. Each of these can be calculated by their particular formulas like mean formula, mode formula, median formula. 

About Mean

Among the measures of central tendencies, the mean is one of the measures and it is the average of the given collection of data. It is a mathematical average and can be calculated in various ways which include the arithmetic mean and the geometric mean method. Nevertheless, all the methods of calculating a simple average give the same results approximately.

Mean = (sum of the values/total number of values)

Example:

Find mean of 2,4,6,8,10.

Solution: Firstly, add the numbers 

2+4+6+8+10 = 30

Total number of values: 5 

Mean= 30/5 = 6 

Symbol of mean: The symbol of the mean is the X bar. The bar represents the mean of the total number of values which are denoted by X. 

Mean formula 

The mean formula is calculated on the given collection of data and each value is considered during evaluation.

The mean formula: sum of given values/Total number of values

For calculation of the arithmetic mean of a collection of data, firstly add all the given data sets (x) then divide it by the total number of data sets (n).

The data values given can be of two types:

1. Grouped data 
2. Ungrouped data 

Both ways have different formulas to calculate the mean.

Types of mean

There are three types of mean in statistics that are listed below:

1. Arithmetic means: When all the data values are added and then divided by the total number of data values, it is known as the arithmetic mean.
2. Geometric mean: In the geometric mean, first all the given numbers in the data are multiplied and take the nth root of all the numbers multiplied where n is the total number of data sets.
3. Harmonic mean: In the harmonic mean, first we reciprocate each of the given values then find the average of them.

The above three types of the mean are known as Pythagorean means.

Median

This is the central score of any given data or distribution. For calculation of the median, first, arrange the given numbers in numerical order and count them. If the counted value is an odd number then divide it by 2. If the value of the division comes in a decimal number then round it off. If the counted value is even then divide it by 2, then check the number in that particular position and average the number with the value present in the higher position of that number.

Mode

Mode is the number that occurs very frequently in a given set of data. To find the mode just check the frequency of the numbers. The number with the highest frequency is the answer.

In cases of a huge set of data, you need to create a frequency distribution table. If there are two modes in a particular data then it is known as bi-modal which means two numbers having the same frequency.

Conclusion

This is a basic topic which you need to know as it can be asked in various examinations. It is not tough to understand, you need to know the formulas to solve the problems. Regular practice is the key to ace this topic.