Arithmetic Mean Formula with Solved Examples

Arithmetic Mean Formula:

An arithmetic mean is the average of the sum total of the given data set. 

The arithmetic mean is also misunderstood as the average of the given numbers, but it is different from the arithmetic mean. To find the arithmetic mean of the data set, one needs to add all the given numbers and divide it by the total frequencies of the data set. The arithmetic mean is represented by X. The formula to find arithmetic mean is 

X=   (i=1nXi)/N 

which means summation of the given data till n divided by total number of observations.

Examples:

 1. In a maths test, the marks obtained out of 70 by 7 students are as follows:

22, 27, 42, 35, 14, 54, 57. Find the arithmetic mean of the marks obtained by the 7 students.

To find the arithmetic mean,

X= 22 + 27 + 42 + 35 + 14 + 54 + 57/7  = 35.8

So, the arithmetic mean of the 7 students in maths test is 35.8.

  2. The arithmetic mean of the 5 observations is 50. Four among the five observations are given, i.e., 20, 35, 55, 40. Find the missing observation.

To find the arithmetic mean,

X= 20+35+55+40+a5 

50 = 20+35+55+40+a5 

Therefore, a = (50 x 5) – (20 + 35 + 55 + 40)

a = 250 – 150

So, a = 100.

 3. Find the arithmetic mean for the observations: 33 + 52 + 65 + 40 + 35

To find the arithmetic mean,

X= (33 + 52 + 65 + 40 + 35)/ 5

Therefore, arithmetic mean for the given observations is X= 225.

 4. The arithmetic mean of the prices of a commodity over 12 months is as 556. The prices for 11 months out of 12 months are given: 400, 425, 541, 478, 436, 525, 500, 498, 475, 436, 512. Find the price for the missing month.

To find the arithmetic mean,

X= (400 + 425 + 541 + 478 + 436 + 525 + 500 + 498 + 475 + 436 + 512 + a)/ 12

556 = (400 + 425 + 541 + 478 + 436 + 525 + 500 + 498 + 475 + 436 + 512 + a)/ 12

(556 x 12) – (400 + 425 + 541 + 478 + 436 + 525 + 500 + 498 + 475 + 436 + 512) = a

a = 6672 – 5226

Therefore, a = 1446.