Answer

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**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 $.

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