Question

A data has the highest value 120 and the lowest value 71. A frequency distribution in descending order with seven classes is to be constructed. The limits of the second class interval shall be
A. 77 and 78
B. 78 and 85
C. 106 and 113
D. 113 and 120

Answer 1

Hint: First find the range of the frequency distribution by subtracting the lowest value from the highest value. We have to divide the distribution into seven classes, so divide the range obtained by 7 to get the width of each class interval. Then subtract 7 from the highest value to get the lower limit of the first class interval and the highest value will be the upper limit and continue this for the seven class intervals to get the limits of the second class interval.

Complete step-by-step answer:
We are given that a data has the highest value 120 and the lowest value 71 and a frequency distribution in descending order with seven classes is to be constructed using this data.
We have to find the limits of the second class interval.
The range of the frequency distribution is the highest value minus the lowest value which is $ 120 - 71 = 49 $
This range must be divided into seven classes. The width of each class interval is
$\Rightarrow \dfrac{{49}}{7} = 7 $
And the class intervals must be constructed in a descending order.
So the first class interval ranges from
$\Rightarrow \left( {120 - 7} \right) $ to 120, which is from 113 to 120. The lower limit is 113 and upper limit is 120.
As the distribution is happening in descending order, the upper limit of the next class interval will be the lower limit of the previous class interval.
So the second class interval’s upper limit is 113 and the lower limit is
$\Rightarrow \left( {113 - 7} \right) = 106 $
In the same way the third class interval’s upper limit is 106 and the lower limit is $ \left( {106 - 7} \right) = 99 $
Therefore, the limits of the second class interval will be 106 and 113.

So, the correct answer is “Option C”.

Note: When the frequency distribution must be constructed in ascending order, the lower limit of the next class interval will be the upper limit of the previous class interval. So be careful with how the frequency distribution must be constructed.