The table above shows the frequency distribution of the heights of 80

I need one explanation. If we take 160 and 144 then we lose data from the table. So, Is it correct to chose then as range.

Aditya Sharma

To minimize the range of heights, the students in group 140-144 should have a height of 144 and in group 160-164 should have a height of 160 cm.
So range = 160 - 144 = 16

Answer B

Should be B. Difference between Highest of 1st row and lowest of last row

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If anyone could please explain me, what does the statement "range of heights" mean?

Hi priyamba,

Note:
1) Range of a discrete data set=maximum value-Minimum value.
2) Range of the numbers in a group of data is the greatest number in the group minus the least number in the group.

Here "Range of heights" implies the difference between maximum and minimum height of the grouped data.
Here we have to find out the minimum of the above difference value. We can't exclude any interval of data sets or heights.

From the frequency distribution table:-
The highest value of height varies from 160-164
The lowest value of height varies from 140-144

Minimum possible range of height=minimum value of height in the interval 160-164 - maximum value of height in the interval 140-144=160-144=16

For more clarity, we may assume that all the 6 students in the interval 140-144 have height of 144.And all the 4 students in the interval 160-164 have height of 160.This is assumed in order to have a minimum difference between max height and min height.By this way,we converted the grouped data to a discrete data set. Now the least possible range of heights= maximum height-minimum height =160-144=16

Hope it helps.

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