How to find Arithmetic Mean in Central Tendency?

In layman’s terms, statistics refers to the process of obtaining, classifying, examining, interpreting, and finally presenting facts in an accessible manner so that one may make an opinion and, if required, take action. 

Examples:

• A teacher gathers students’ grades, organizes them in ascending or decreasing order, calculates the average class grade, or finds the number of pupils who failed and informs them so that they begin studying harder.
• Officials from the government are gathering data for the census and comparing it to past records to determine if population growth is under control or not.

Central Tendency

A central tendency is a centre or typical value for a probability distribution in statistics. Averages are a common term for measurements of central tendency. Arithmetic mean is the most popular value of central tendency for a statistical series. Although median and mode are also prevalent, the significance of arithmetic mean outweighs both those measures, even when combined together.

How to find Arithmetic Mean in Central Tendency?

Answer:

Arithmetic Mean

Arithmetic mean, also known as average, is derived for a given collection of data by summing the numbers in the data and dividing the result by the number of observations. It is the most often used central tendency approach.

Formula

The following formula is used to determine the arithmetic mean:

Sum total of the terms divided by the number of such terms

So the arithmetic mean of a statistical series with n number of observations is given by:

X = Σx/N.

Sample Questions

Question 1: Find the mean of 1, 3, 8, 7, 9.

Solution:

Mean = 1+ 3 + 8 + 7 + 9/ 5

= 28/ 5

= 5.6

Question 2: Find the arithmetic mean of: 7, 18, 121, 51, 101, 81, 1, 19, 9, 10, 16.

Solution:

Mean = 7 + 18+ 121 + 51 + 101 + 81 + 1 + 19 + 9 + 10 + 16/ 11

= 434/ 11

= 39.454

Question 3: Find the arithmetic mean of 9, 7, 7, 8, 7, 2, 8, 5, 6, 4.

Solution:

Mean = 9 + 7 + 7 + 8 + 7 + 2 + 8 + 5 + 6 + 4/ 10

= 63/10

= 6.3

Question 4: Find the arithmetic mean of 9, 7, 7, 8, 7, 2, 8, 3, 6, 4.

Solution:

Mean = 9 + 7 + 7 + 8 + 7 + 2 + 8 + 3 + 6 + 4/ 10

= 61/10

= 6.1

Question 5: Find the arithmetic mean of 9, 6, 7, 8, 7, 2, 8, 3, 6, 4.

Solution:

Mean = 9 + 6 + 7 + 8 + 7 + 2 + 8 + 3 + 6 + 4/ 10

= 60/10

= 6