A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent

Solution:

We will use Assumed Mean Method to solve this question because the data given is large.

When the numerical values of xᵢ and fᵢ are large, then finding the product of xᵢ and fᵢ becomes tedious. We can change each xᵢ to a smaller number so that our calculations become easy. Now we have to subtract a fixed number from each of these xᵢ.

• The first step is to choose one value among xᵢ as the assumed mean and denote it by ‘ a ’. Also, to further reduce our calculation work, we may take ‘ a ’ to be that xᵢ which lies in the center of x₁, x₂, . . ., xₙ. So, we can choose a.
• The second step is to find the difference ‘ dᵢ ’. That is the difference between a and each of the xᵢ. The deviation of ‘ a ’ from each of the xᵢ. i.e., dᵢ = xᵢ - a
• The third step is to find the product of dᵢ with the corresponding fᵢ_. After that take the sum of all the fᵢdᵢ.

Now use the values in the below formula

Mean, (x) = a + Σfᵢdᵢ/ Σfᵢ

We know that, Class mark, xᵢ = (Upper class limit + Lower class limit )/2

Taking assumed mean, a = 17

From the table, we obtain, Σfᵢ = 40 and Σfᵢuᵢ = - 181

Mean, (x) = a + (Σfᵢdᵢ/ Σfᵢ) 

= 17 + (- 181/40)

= 17 - 4.525

= 12.475

≈ 12.48

Thus, the mean number of days a student was absent is 12.48

☛ Check: NCERT Solutions for Class 10 Maths Chapter 14

Video Solution:

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.1 Question 8

Summary:

The mean number of days a student was absent based on the absentee record of 40 students of a class for the whole term is 12.48 using the assumed mean method.

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