Question

Question 6
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data.

$\begin{array}{ccccccccc}\text{Number of cars}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 7& 14& 13& 12& 20& 11& 15& 8\end{array}$

Answer 1

From the given data, we may observe that maximum class frequency is 20 belonging to 40 - 50 class intervals.

So, modal class = 40 - 50

Lower limit $l$ of modal class = 40

Frequency $\left(f_1\right)$ of modal class = 20

Frequency $\left(f_0\right)$ of class preceding modal class = 12

Frequency $\left(f_2\right)$ of class succeeding modal class = 11

Class size = 10

$mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h=40+\left[\frac{20-12}{2\left(20\right)-12-11}\right]\times 10=40+\left(\frac{80}{40-23}\right)=40+\frac{80}{17}$

= 40 + 4.7

= 44.7

So, mode of this data is 44.7 cars.