Question

The following histogram shows the frequency distribution f the ages of 22 teachers in a school:


(i) What is the number of eldest and youngest teachers in the school?
(ii) Which age group teachers are more in the school and which least?
(iii) What is the size of the classes?
(iv) What are the class marks of the classes?

Answer 1

(i) The eldest (50$-$55 years) = 1 person
This is because the height of the rectangle with class interval 50$-$55 as base is 1 unit.
The youngest (20$-$25 years)= 2 persons
This is because the height of the rectangle with class interval 20$-$25 as base is 2 units.

(ii) The group containing the most number of teachers is 35$-$40 years. This is because the height of the rectangle with class interval 35$-$40 as base is the maximum.
The group containing the least number of teachers is 50$-$55 years. This is because the height of the rectangle with class interval 50$-$55 as base is the minimum.

(iii) Class size = The range between the upper and the lower boundaries of the class
For example, the size of the class 20$-$25 years is 5.

(iv) $\mathrm{Class}\mathrm{mark}=\frac{\mathrm{Upper}\mathrm{limit}+\mathrm{Lower}\mathrm{limit}}{2}$
$$\begin{gathered} \mathrm{For}\mathrm{class}20-25: \\ \mathrm{Class}\mathrm{mark}=\frac{20+25}{2}=\frac{45}{2}=22.5 \end{gathered}$$
Similarly, the class marks of the other classes are 27.5; 32.5; 37.5; 42.5; 47.5; 52.5.