Solved Examples on Arithmetic Mean
Example 1: Find the arithmetic mean of the first five prime numbers.
Solution:
Arithmetic mean of first five prime numbers,
First Five Prime Numbers = 2, 3, 5, 7 and 11
Number of observations (n) = 5
Mean (x̄) = (Sum of Observations)/ (Number of Observations)
x̄ = (2 + 3 + 5 + 7 + 11)/5 = 28/5
x̄ = 5.6
Hence, the arithmetic mean of the first five prime numbers is 5.6.
Example 2: If the arithmetic mean of five observations 5, 6, 7, x, and 9 is 6. Find the value of x.
Solution:
Given observations are 5, 6, 7, x, and 9
Number of Observations = 5
Mean (x̄) = (Sum of Observations)/ (Number of Observations)
6 = (5 + 6 + 7 + x + 9)/5
30 = 27 + x
x = 30 – 27
x = 3
Hence, the value of x is 3
Example 3: If the arithmetic mean of five observations 10, 20, 30, x, and 50 is 30. Find the value of x.
Solution:
Given, observations are 10, 20, 30, x and 50
Number of observations = 5
Mean (x̄) = (Sum of Observations)/ (Number of Observations)
30 = (10 + 20 + 30 + x + 50)/5
150 = 110 + x
150 – 110 = x
x = 40
Hence, the value of x is 40
Arithmetic Mean
Arithmetic Mean is defined as the ratio of all the values or observations to the total number of values or observations. Arithmetic Mean is one of the fundamental formulas used in mathematics and it is highly used in various solving various types of problems. We can understand it with some examples, if in a family the husband earns 35,000 rupees and his wife earns 40,000 rupees then what is their average salary? This average is also called the arithmetic mean of 35,000 rupees and 40,000 rupees, which is calculated by adding these two salaries and then dividing it by 2.
Average Salary (Arithmetic Mean of Salary) = (35000 + 40000)/2 = 37500.
Thus, the arithmetic mean is used in various scenarios such as in finding the average marks obtained by the student in marks, the average rainfall in any area, etc.