Question

The class marks of a distribution are \[62,67,72,77,82\] and \[87\]. Find the class-size and class-limits.
A. Class size \[ = 7\]; Class limits: \[59.5 - 64.5,64.5 - 69.5,69.5 - 74.5,74.5 - 79.5,79.5 - 84.5\] and \[84.5 - 89.5\]
B. Class size\[ = 5\]; Class limits: \[59.5 - 64.5,64.5 - 69.5,69.5 - 74.5,74.5 - 79.5,79.5 - 84.5\] and \[84.5 - 89.5\]
C. Class size\[ = 9\]; Class limits: \[59.5 - 64.5,64.5 - 69.5,69.5 - 74.5,74.5 - 79.5,79.5 - 84.5\] and \[84.5 - 89.5\]
D. None of these.

Answer 1

Hint: Subtract the given data from one observation to another to get the class size. Find the half of class size, then subtract it and add it to each observation to get the lower limit and upper limit of a class interval respectively.

Complete step by step solution:
The class size is the average number of elements per class which is calculated by subtracting the upper limit of a class interval by the lower limit. It is the number of elements that implies, if it is an inclusive function, it means, the class size is the difference between the true upper limit and the true lower limit of the class interval.
Now, since the class size is obtained by subtracting the two consecutive observations, we have:
Class size \[ = 67 - 62 = 72 - 67 = 5\]
Here, the difference between all the observations remain the same making the class size a constant.
Therefore, Class size \[ = 5\]
Now,
Class intervals are obtained by subtracting the half of class size to form the lower limit and adding the half of class size to form the upper limit.
Half of class size \[ = \dfrac{5}{2}\] \[ = 2.5\]
First interval \[ = \]\[(62 - 2.5 = 59.5) - (62 + 2.5 = 64.5)\]
\[ \Rightarrow 59.5 - 64.5\]
Second interval \[ = (67 - 2.5 = 64.5) - (67 + 2.5 = 69.5)\]
\[ \Rightarrow 64.5 - 69.5\]
Third interval \[ = (72 - 2.5 = 69.5) - (72 + 2.5 = 74.5)\]
\[ \Rightarrow 69.5 - 74.5\]
Fourth interval \[ = (77 - 2.5 = 74.5) - (77 + 2.5 = 79.5)\]
\[ \Rightarrow 74.5 - 79.5\]
Fifth interval \[ = (82 - 2.5 = 79.5) - (82 + 2.5 = 84.5)\]
\[ \Rightarrow 79.5 - 84.5\]
Sixth interval \[ = (87 - 2.5 = 84.5) - (87 + 2.5 = 89.5)\]
\[ \Rightarrow 84.5 - 89.5\]
Therefore, we have the intervals, \[59.5 - 64.5,64.5 - 69.5,69.5 - 74.5,74.5 - 79.5,79.5 - 84.5\] and \[84.5 - 89.5\].

$\therefore $ The correct option is B.

Note: Class intervals are the subsets into which the data is grouped. The width of the class intervals will be the difference between the class upper limit and the class lower limit. The intervals can be of any width but to make it simpler and more organised, we group the data having more frequency of a group into one interval to avoid only one observation per interval which is not useful.