Question

The frequency distribution of driving speeds (in km/hr) of the vehicles of 400 college students is given below.

Speed (in kms/hr)	20-30	30-40	40-50	50-60	60-70
No. of students	6	80	156	98	60

Find the modal driving speed.

Answer 1

Speed (in km/hr)	No. of students (frequency)
20-30	6
30-40	80
40-50	156
50-60	98
60-70	60

Here, the maximum frequency f_m is 156. So, the corresponding modal class is 40-50
Mode = L+$\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h$
Here, L = lower limit of the modal class =40
$f_m=$maximum frequency = 156
$f_1=$frequency of pre-modal class = 80
$f_2=$frequency of post-modal class = 98
h = width of modal class = 10
$$\begin{gathered} \therefore \mathrm{Mode}=40+\left[\frac{156-80}{2\left(156\right)-80-98}\right]\times 10 \\ =40+\left[\frac{76}{312-80-98}\right]\times 10 \\ =40+\frac{76}{134}\times 10 \\ =40+5.67 \\ =45.67 \\ \therefore \mathrm{The}\mathrm{modal}\mathrm{driving}\mathrm{speed}\mathrm{is}45.67\mathrm{km}/\mathrm{hr}. \end{gathered}$$