Question

What is the class mark of a class a-b?

Answer 1

Hint: Understand the definition of class mark and assume ‘a’ as the lower limit and ‘b’ as the upper limit of the interval a-b and apply the formula: class mark = $\dfrac{a+b}{2}$ to get the answer.

Complete step by step answer:
Here, we have been provided with an interval a-b and we have been asked to determine the value of class marks. But first, let us learn about class marks and class limits.
Classmark is defined as the average value or mid-point value of a given interval in a frequency distribution. Classmark is also called class midpoint. In other words, we can say that class marks are the average of the upper-class limit and the lower class limit. So, let us see what are class limits.
When we talk about class limits, they are of two types, namely, lower class limit and upper-class limit. The lower class limit denotes the minimum value of data that can be included in an interval while the upper-class limit denotes the maximum value of data that can be entered in that interval. To find these two types of class limits, we use the formulas
Lower class limit = class mark - $\dfrac{\text{class size}}{2}$
Upper class limit = class mark + $\dfrac{\text{class size}}{2}$
The above formulas are used when we have not been provided with intervals. But in the given question, we have been provided with an interval a-b. So, we have
\[\Rightarrow \] class mark = $\dfrac{1}{2}\times $ (upper class limit + lower class limit)
\[\Rightarrow \] class mark = $\dfrac{1}{2}\times $ (a + b)
Hence, the class mark of the interval a-b is $\dfrac{a+b}{2}$ .

Note:
 One must not get confused in the expression a-b and do not consider it as the difference of two terms a and b. This expression actually denotes the data interval whose minimum value is ‘a’ and the maximum value is ‘b’. You must remember the definitions of basic terms of statistics like – class size, classmark, class limits etc, to solve the question.