Question

Compute the mode from the following data:
$\begin{array}{ccccccccccc}\text{Class}& & & & & & & & & & \\ \text{interval}& 1-5& 6-10& 11-15& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45& 46-50\\ \text{Frequency}& 3& 8& 13& 18& 28& 20& 13& 8& 6& 4\end{array}$

Answer 1

The given series is converted from inclusive to exclusive form and on preparing the frequency table, we get

Class	Frequency
0.5-5.5	3
5.5-10.5	8
10.5-15.5	13
15.5-20.5	18
20.5-25.5	28
25.5-30.5	20
30.5-35.5	13
35.5-40.5	8
40.5-45.5	6
45.5-50.5	3

As the class 20.5-25.5 has a maximum frequency, so it is the modal class:

Therefore,
l=20.5, h=5, f=28 and f1=18 and f2=20

Mode = l+[h×(f−f1)/(2f−f1−f2)]

=20.5+[5×(28−18)/(2×56−18−20)]

= 20.5 + [5 x 10 /18]

= 20.5 + 2.78 = 23.28

Hence, mode = 23.28