Question

The Sturges rule for determining the number of classes $\left( n \right)$ in a frequency distribution with total frequency $N$ is
(A) $n = 1 + 2.3108\,N$
(B) $N = 1 + 3.3108\,N$
(C) $n = 1 + 3.3\log \,N$
(D) $n = 1 - 3.3\log \,N$

Answer 1

Hint: In this question we just have to recall the formula of Sturges rule and then we will put the value of number of classes , the value of total frequency in the Sturges rule. The Sturges rule is used to determine the number of classes when the total number of observations is given.

Formula used: Sturges rule to find the number of classes is given by $K = 1 + 3.322\log \,N$ where $K$ is the number of classes and $N$ is the total frequency.

Complete step-by-step solution:
The number of classes given in the question is $n$ and total frequency is $N$
We know that Sturges rule is used to find the number of classes which is used in a histogram or frequency distribution.
From Sturges rule we can write.
$K = 1 + 3.322\log \,N$
Put the values of number of classes and total frequency in the above equation. Therefore, we will get
$n = 1 + 3.322\log \,N$
We can write the above equation as $n = 1 + 3.3\log \,N$ .

Hence, the correct option is (C).

Additional information: we will see in this example how to apply Sturges rule. Example: If the total number of observations are $1000$ then we can find the number of classes by the Sturges rule $K = 1 + 3.322\log \,N$
$
   \Rightarrow K = 1 + 3.322\log 1000 \\
   \Rightarrow K = 1 + 3.322\left( 3 \right) = 10.966
 $

Note: The important thing in this question is the rule given by Sturges which we have to remember. The Sturges rule is the function of $\log $ so while solving the question related to Sturges rule just make sure that we are comfortable with the properties of $\log $.