Question

The Sturges rule for determining the number of classes $\left(n\right)$ in a frequency distribution with total frequency $N$ is
(A) $n=1+2.3108N$
(B) $N=1+3.3108N$
(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 $K=1+3.322\log N$
$$\begin{gathered} \Rightarrow K=1+3.322\log 1000 \\ \Rightarrow K=1+3.322\left(3\right)=10.966 \end{gathered}$$

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 $\log$.