Question

The class mark of the interval \[60 - 70\] is
A.\[60\]
B.\[70\]
C.\[65\]
D.\[72\]

Answer 1

Hint: Class mark is the average of end limits of an interval. In the question lower limit and upper limit are given as \[60\] and \[70\] respectively. So to find the class mark, we can simply average the two values with very simple calculation. Class mark is similar to median except for the fact that median is found out in the overall distribution whereas class mark is found out for an interval within the data.

Complete step-by-step answer:
In an interval the lower limit and the upper limit are \[60\] and \[70\] respectively.
Class mark is defined so as to find the middle value of an interval or the closest value to the middle value of interval. Although by its formula, it is simply the average of the upper and lower limit of the interval.
Thus, let’s denote the class mark by \[x\] , lower limit by \[l\] and upper limit by \[u\].
Thus, \[l = 60\] and \[u = 70\].
Now, by definition of class mark, its formula can be written as \[x = \dfrac{{u + l}}{2}\].
We can now substitute the values of \[u\] and \[l\] in the above formula as
\[
   \Rightarrow x = \dfrac{{u + l}}{2} \\
   \Rightarrow x = \dfrac{{70 + 60}}{2} \\
   \Rightarrow x = \dfrac{{130}}{2} \\
   \Rightarrow x = 65 \\
\]
Thus, the class mark comes out to be \[65\].
Hence, option (C) is the correct option.

Note: Another way of solving is by analyzing the options. If we are finding the class mark of an interval than it will lie within the interval itself, so if the lower and upper limits are \[60\] and \[70\] respectively, then the class mark must lie in between the interval and there is only one option where this is true, that is option (C). But this is possible only if multiple choices are given.