**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?

**Solution:**

(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) Class mark $=\frac{\text { Upper limit }+\text { Lower limit }}{2}$

For class $20-25$ :

Class mark $=\frac{20+25}{2}=\frac{45}{2}=22.5$

Similarly, the class marks of the other classes are 27.5; 32.5; 37.5; 42.5; 47.5; 52.5.