Question

Find the class mark of classes 15.5 – 18.5 and 50 – 75.

Answer 1

Hint: First we will understand the terms ‘class mark’ and then we will solve the two subparts of the question one by one. Now, first consider the class interval 15.5 – 18.5 and compare it with the class interval a – b, where ‘a’ is called the lower limit and ‘b’ is called the upper limit of the class interval. Use the formula: - Class mark = $\dfrac{a+b}{2}$ to get the answer. Apply the same process for the class interval 50 – 75.

Complete step by step answer:
Here we have been provided with two class intervals 15.5 – 18.5 and 50 – 75, we are asked to find the class mark of both the intervals. First we need to know about the term ‘class mark’.
In mathematics, class mark is defined as the average or arithmetic mean of the lower and upper limit of a class interval. Suppose we have a class interval a – b where ‘a’ is the lower limit and ‘b’ is the upper limit of the class interval, therefore the class mark is given as: - Class mark = $\dfrac{a+b}{2}$. Let us solve for the two subparts of the question one by one.
(1) Here we have the class interval 15.5 – 18.5, so comparing it with a – b we have a = 15.5 and b = 18.5. Therefore, substituting the values in the formula we get,
$\Rightarrow $ Class mark = $\dfrac{15.5+18.5}{2}$
$\Rightarrow $ Class mark = $\dfrac{34.0}{2}$
$\therefore $ Class mark = 17
(2) Here we have the class interval 50 – 75, so comparing it with a – b we have a = 50 and b = 75. Therefore, substituting the values in the formula we get,
$\Rightarrow $ Class mark = $\dfrac{50+75}{2}$
$\Rightarrow $ Class mark = $\dfrac{125}{2}$
$\therefore $ Class mark = 62.5
Hence, the class mark of the interval 15.5 – 18.5 is 17 and that of the interval 50 – 75 is 62.5.

Note: You must remember some basic terms of statistics like: - class mark, class interval, class height or class size. These terms are used in grouped data statistics. Note that if we are asked to calculate the class size then we take the difference of the upper limit and the lower limit to get the value. In a grouped frequency table we have to determine these values to calculate the mean, median and mode.