Question

The class marks of a distribution are $26,31,36,41,46,51,56,61,66,71$. Find the true class limits.

Answer 1

Hint: Here we have to find out the true class limits of the given set of observations, which are the class marks of a distribution. The class marks mean the average of the upper limit and the lower limit of a class. But here just the class marks are given, not the class intervals of a particular range. So here in order to find the class interval of a class from the class mark has to be figured out.

Complete step-by-step solution:
Here, given the class marks of the distribution.
No. of class marks given = 10
$\therefore $There are going to be 10 class intervals.
Now as the 10 class marks have a common difference between the consecutive terms which is 5.
$\therefore $The class width of a class interval is 5
We can find the upper limit and the lower limit of a class from the class mark by dividing the class width by 2 and then subtracting it from the class mark gives the lower limit of the class, while adding it to the class mark gives the upper limit of the class. For a better understanding it is expressed mathematically below:
$ \Rightarrow $Lower limit = class mark - $\dfrac{5}{2}$
$ \Rightarrow $Upper limit = class mark + $\dfrac{5}{2}$
The class range of the class mark 26 is given by:
$ \Rightarrow $Lower limit = \[26 - \dfrac{5}{2} = 23.5\]
$ \Rightarrow $Upper limit = \[26 + \dfrac{5}{2} = 28.5\]
The class range of the class mark 31 is given by:
$ \Rightarrow $Lower limit = \[31 - \dfrac{5}{2} = 28.5\]
$ \Rightarrow $Upper limit = \[31 + \dfrac{5}{2} = 33.5\]
The class range of the class mark 36 is given by:
$ \Rightarrow $Lower limit = \[36 - \dfrac{5}{2} = 33.5\]
$ \Rightarrow $Upper limit = \[36 + \dfrac{5}{2} = 38.5\]
The class range of the class mark 41 is given by:
$ \Rightarrow $Lower limit = \[41 - \dfrac{5}{2} = 38.5\]
$ \Rightarrow $Upper limit = \[41 + \dfrac{5}{2} = 43.5\]
The class range of the class mark 46 is given by:
$ \Rightarrow $Lower limit = \[46 - \dfrac{5}{2} = 43.5\]
$ \Rightarrow $Upper limit = \[46 + \dfrac{5}{2} = 48.5\]
The class range of the class mark 51 is given by:
$ \Rightarrow $Lower limit = \[51 - \dfrac{5}{2} = 48.5\]
$ \Rightarrow $Upper limit = \[51 + \dfrac{5}{2} = 53.5\]
The class range of the class mark 56 is given by:
$ \Rightarrow $Lower limit = \[56 - \dfrac{5}{2} = 53.5\]
$ \Rightarrow $Upper limit = \[56 + \dfrac{5}{2} = 58.5\]
The class range of the class mark 61 is given by:
$ \Rightarrow $Lower limit = \[61 - \dfrac{5}{2} = 58.5\]
$ \Rightarrow $Upper limit = \[61 + \dfrac{5}{2} = 63.5\]
The class range of the class mark 66 is given by:
$ \Rightarrow $Lower limit = \[66 - \dfrac{5}{2} = 63.5\]
$ \Rightarrow $Upper limit = \[66 + \dfrac{5}{2} = 68.5\]
The class range of the class mark 71 is given by:
$ \Rightarrow $Lower limit = \[71 - \dfrac{5}{2} = 68.5\]
$ \Rightarrow $Upper limit = \[71 + \dfrac{5}{2} = 73.5\]
Thus the class intervals are:
$23.5 - 28.5,$
$28.5 - 33.5,$
$33.5 - 38.5,$
$38.5 - 43.5,$
$43.5 - 48.5,$
$48.5 - 53.5,$
$53.5 - 58.5,$
$58.5 - 63.5,$
$63.5 - 68.5,$
$68.5 - 73.5.$

Note: Please note that as the class intervals are formed from the class marks. Hence these limits are the true class limits.