Question

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students
Age (in years):
15
16
17
18
19
20
No. of students:
3
8
10
10
5
4

Answer 1

ARITHMETIC MEAN OR MEAN OR AVERAGE :  

The arithmetic mean of a set of observations is obtained by dividing the sum of the values of all observations by the total number of observations .

Mean = Sum of all the observations / Total number of observations .

MEAN = Σfixi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfixi = 698 , Σfi = 40

MEAN = Σfixi / Σfi  

MEAN = 698/40 = 17.45

MEAN = 17.45

Hence, the mean age of the students = 17.45 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The mean is 17.45 .

Step-by-step explanation :

Arithmetic Mean -

Mean of a set of observations is obtained by dividing the sum of all observations by the total number of observations .

Mean = Sum of all observations / Total observations .

$Mean=\frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$

where $\Sigma$ means summation.

Frequency Distribution Table -

$\begin{tabular}{| c | c | c |}\cline{1-3}Age(x_{i}) & No.\:of\:students(f_{i}) & f_{i}x_{i} \\ \cline{1-3}15 & 3 & 45 \\ \cline{1-3}16 & 8 & 128 \\ \cline{1-3}17 & 10 & 170 \\ \cline{1-3}18 & 10 & 180 \\ \cline{1-3}19 & 5 & 95 \\ \cline{1-3}20 & 4 & 80 \\ \cline{1-3} & \Sigma f_{i}=40 & \Sigma f_{i}x_{i}=698 \\ \cline{1-3}\end{tabular}$

Since, mean -

$\implies\frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$

$\implies Mean=\frac{698}{40}$

$\implies 17.45$