Question

Below is given frequency distribution of driving speed (in kms/hour) of a vehicle of $400$ college students.

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

Find modal driving speed of college students.

• A. $41.67$ kms/hour
• B. $45.67$ kms/hour
• C. $49.67$ kms/hour
• D. $53.67$ kms/hour

Answer 1

Answer: (B)

$45.67$ kms/hour

The modal group is $40-50$.
Estimated Mode $=$ $L+\left(\frac{f_m-f_{m-1}}{(f_m-f_{m-1})+(f_m-f_{m+1})}\right)\times w$
where:
$L$ is the lower class boundary of the modal group
$f_{m-1}$ is the frequency of the group before the modal group
$f_m$ is the frequency of the modal group
$f_{m+1}$ is the frequency of the group after the modal group
$w$ is the group width
Estimated Mode $=$ $L+\left(\frac{f_m-f_{m-1}}{(f_m-f_{m-1})+(f_m-f_{m+1})}\right)\times w$
Mode $=$ $40+\left(\frac{156-80}{(156-80)+(156-98)}\right)\times 10$
Mode $=$ $40+\left(\frac{76}{134}\right)\times 10$
Mode $=45.67$