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.

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

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Solution

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 $(f_{1})$ of modal class = 20

Frequency $(f_{0})$ of class preceding modal class = 12

Frequency $(f_{2})$ of class succeeding modal class = 11

Class size = 10

$m o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h = 40 + [\frac{20 - 12}{2 (20) - 12 - 11}] \times 10 = 40 + (\frac{80}{40 - 23}) = 40 + \frac{80}{17}$

= 40 + 4.7

= 44.7

So, mode of this data is 44.7 cars.

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

Number of cars:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	7	14	13	12	20	11	15	8

Q. A student noted the number of cars passing through a spot on a road for

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periods each of

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Number of cars	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	$7$	$14$	$13$	$12$	$20$	$11$	$15$	$8$

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.

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