Question:
The following is the distribution of height of students of a certain class in a certain city:
Find the average height of maximum number of students.
Solution:
The given data is an inclusive series. So, firstly convert it into an exclusive series as given below.
Here, the maximum frequency is 142 so the modal class is 165.5−168.5.
Therefore,
$l=165.5$
$h=3$
$f=142$
$f_{1}=118$
$f_{2}=127$
Now,
Mode $=l+\frac{f-f_{1}}{2 f-f_{1}-f_{2}} \times h$
$=165.5+\frac{142-118}{284-118-127} \times 3$
$=165.5+\frac{24}{39} \times 3$
$=165.5+\frac{24}{13}$
$=165.5+1.85$
$=167.35$
Thus, the average height of maximum number of students is 167.35 cm.
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