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Question 11 Classification And Tabulation Of Data Graphical Representation Of Data As Histograms Exercise 24.1

The following histogram shows the frequency distribution of 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:

(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) The class mark is the mid-point of the class interval. i.e., Class mark = (upper limit + lower limit) / 2

Hence, the class mark of each class is as follows:

For Class 20 – 25:

Class mark = (20+25)/2 = 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.

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