Question

Find the class mark of class 20 – 30 and 30 – 40.

Answer 1

Hint: In this question, we are given a class interval and we have to find the class mark of the given class interval. As we know, the class mark is the middle value of any interval, hence for calculating the class mark we will take the average of the lower term of the interval and upper term of the interval. The average is taken by first finding the sum of lower limit interval and upper limit of interval and then dividing it by two.

Complete step-by-step answer:
Before solving the question, let us first understand what a class interval is. Class intervals are subset into which data is grouped. The width of the class interval is the difference between the lower limit of the interval and the upper limit of the interval. For easier calculations, we find the mid-value of class-interval which is called a class mark. Class mark is defined as the average of the upper- and lower class limits.
Here, we are given the first-class interval as 20 – 30, which means the lower limit of this class interval is 20 and the upper limit of the class interval is 30. The second-class interval is 30 – 40, which means the lower limit of this class interval is 30 and the upper limit of the class interval is 40.
We need to find the class mark for this class interval.
Since the class mark of a class interval is given by dividing the sum of the lower limit of class and upper limit of the class interval by 2. So, we get
Class Mark $ = \dfrac{{lower\,limit + upper\,limit}}{2}$
For interval 20 – 30, substitute the values,
$ \Rightarrow $ Class Mark $ = \dfrac{{20 + 30}}{2}$
Add the terms in the numerator,
$ \Rightarrow $ Class Mark $ = \dfrac{{50}}{2}$
Divide numerator by denominator,
$\therefore $ Class Mark $ = 25$
For interval 30 – 40, substitute the values,
$ \Rightarrow $ Class Mark $ = \dfrac{{30 + 40}}{2}$
Add the terms in the numerator,
$ \Rightarrow $ Class Mark $ = \dfrac{{70}}{2}$
Divide numerator by denominator,
$\therefore $ Class Mark $ = 35$

Hence, the class mark for interval 20 – 30 is 25 and for interval 30 – 40 is 35.

Note: Students should always keep in mind that the class marks always lie between given class intervals, that is, it will be greater than the lower limit of class interval and less than the upper limit of the class interval. The class mark of any positive class interval cannot be negative. Students should be careful while doing addition and division. Students should not get confused when a class mark is asked as it is the same as the mid-value of the given class interval.