Question

Find the mid-value of class interval \[30-40\].
$\begin{align}
  & (a)30 \\
 & (b)35 \\
 & (c)5 \\
 & (d)None~of~these \\
\end{align}$

Answer 1

Hint: In this question, we are given a class interval and we have to find mid-value of the given class interval. As we know, mid-value is the middle value of any interval, hence for calculating mid-value we will take the average of the lower term of the interval and middle term of the interval. 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 interval and the upper limit of 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 class interval as $30-40$, 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 mid-value of this class interval, which we need to find the class mark of the given class interval.
Since, class mark of a class interval is given by dividing sum of lower limit of class and upper limit of class interval by $2$, hence we get –
Class mark = Mid-value $=\dfrac{lower~limit+upper~limit}{2}$
$\begin{align}
  & =\dfrac{30+40}{2} \\
 & =\dfrac{70}{2} \\
 & =35 \\
\end{align}$

Hence, the mid-value of a given class interval $30-40$ is $35$.

So, the correct answer is “Option (b)”.

Note: Students should always keep in mind that the mid-value 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 class interval. Mid-value 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.