Elementary Statistics (1+1)

4.2.2.2 Class intervals

The difference between the Upper and Lower limit of a class is known as class interval of that class. For example, in the class 100-200, the class interval is 200-100 = 100. An important decision while constructing a frequency distribution is about the width of the class interval i.e. whether it should be 10,20,50,100,500 etc. The decision would depend upon a number of factors such as the range in the data, i.e. the difference between the smallest and largest item, the details required and number of classes to be formed, etc. A simple formula to obtain the estimate of appropriate class interval, i.e. is

where, L = largest item

S = smallest item

K = the number of classes.

For example, if the salary of 100 employees in a commercial undertaking varied between Rs.500 and Rs.5,500 and we want to form 10 classes, then the class interval would be

L = 5,500, S = 500, k = 10

The starting class would be 500 – 1000, the next 1000-1500 and so on.

The question now is how to fix the number of classes, i.e. The number can be either fixed arbitrarily keeping in view the nature of problem under study or it can be decided using Sturges’ Rule. According to this rule, number of classes can be determined by the formula :

k = 1 + 3.322 log N

where N = total number of observations and

Log = logarithms of the number

Thus, if 10 observations are being studied, the number of classes shall be :

k = 1 + (3.322 x 1) = 4.322 or 4.

and if 100 observations are being studied, the number of classes shall be

k = 1 + (3.322 x 2) = 1 + 6.644 = 7.644 or 8

It should be noted that since log is used in the formula, the number of classes shall generally be between 4 and 20 – it cannot be less than 4 even if N is less than 10 and if N is 10 lakh k will be 1+(3.322x6) = 19.932 or 20.

Sturges suggested the following formula for determining the magnitude of class interval :

Where Range is the difference between the largest and smallest items.

For example, if in the above illustration we apply this formula the magnitude of class interval shall be :

If we take a class interval of 650, the number of classes formed would be 5000/650, i.e. 7.69 or 8.

It may be noted that the application of above formula may give a value involving fractions and odd intervals. For example, we got i=6.541. In such cases suitable approximation should be made.