Question

A grouped frequency distribution table with classes of equal sizes using $63-72$ ($72$ included) as one of the class is constructed for the following data:

$30,32,45,54,74,78,108,112,66,76,88,40,14,20,15,35,44,66,75,84,95,96,102,110,88,74,112,14,34,44.$

The number of classes in the distribution will be:

• A. $9$
• B. $10$
• C. $11$
• D. $12$

Answer 1

The correct option is B

$10$

Explanation for the correct option:

Find the number of classes in the distribution:

Given, The set of data is:

$30,32,45,54,74,78,108,112,66,76,88,40,14,20,15,35,44,66,75,84,95,96,102,110,88,74,112,14,34,44.$

Here, $14$ is the minimum observation and $112$ is the maximum observation.

$\therefore$ Range$=112-14=98$

If one the classes is $63-72$ then the range of the class is $10$ ($72$ included)

Number of classes$=\frac{98}{10}=9.8$, which is near to $10$

Hence, for the given distribution the number of classes is $10$.

Therefore, Option B is correct answer.