Question

 Give the formula for class mark and class size of data.

Answer 1

Hint: To get the formula for the class mark and class size, just follow their definitions. The class mark is the average of the upper and lower limit of a class interval and the class size is the difference of the upper and lower limit of a class interval.

Complete step by step answer:

According to the question, we have to get the formula for the class mark and class size.

We know that class mark is the mid-value or central value of a class. It means that it is the average of the actual upper limit and actual lower limit for a given class. It may also be said that the mid value of every class interval is called its class mark.

The class mark can be calculated by the formula, \[\text{Class}\,\text{Mark=}\dfrac{\text{actual}\,\text{upper}\,\text{limit+actual lower}\,\text{limit}}{\text{2}}\] ………………..(1)

For instance, let us consider the class interval 10-20,

The actual upper limit of the given class = 20 ………….(2)

The actual lower limit of the given class = 10 …………(3)

Now, from equation (1), equation (2), and equation (3), we get

\[\text{Class}\,\text{Mark=}\dfrac{\text{20+10}}{\text{2}}=15\]

Therefore, the class mark for the class interval 10-20 is 15.

We also know that the class size is defined as the difference between the actual upper limit and actual lower of a given class interval.

The class size can be calculated by the formula, \[\text{class}\,\text{size=actual}\,\text{upper}\,\text{limit - actual}\,\text{lower}\,\text{limit}\] ……………………………………(4) 

For instance, again let us consider the class interval 10-20,

The actual upper limit of the given class = 20 ………………………………….(5)

The actual lower limit of the given class = 10 ……………………………………(6)

Now, from equation (4), equation (5), and equation (6), we get

\[\text{Class}\,\text{size=20}-10=10\]

Therefore, the class size for the class interval 10-20 is 10.

From equation (1) and equation (4), we have formula for the class mark and class size for a given class interval respectively.

Hence, \[\text{Class}\,\text{Mark=}\dfrac{\text{actual}\,\text{upper}\,\text{limit+actual lower}\,\text{limit}}{\text{2}}\] and \[\text{class}\,\text{size=actual}\,\text{upper}\,\text{limit - actual}\,\text{lower}\,\text{limit}\] .

Note: In this question, one might get confused and consider class size as the summation of the upper and lower limits of a given class interval. This is wrong because class size is the difference between the upper and lower limits of a given class interval. Therefore, one must keep this point in mind.