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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.

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44.7

55.8

52.8

35.8

answer is A.

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Detailed Solution

The frequency distribution table is given as:
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes

The mode of the data can be obtained by using,

Mode = I + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) h, w h ere

, I is the lower limit of the modal class,

f_{1}

is the frequency of the modal class,

f_{0}

is the frequency of the class preceding the modal class,

f_{2}

is the frequency of the class succeeding the modal class, and h is the class size.
Modal class will be the class which has the highest frequency.
It is observed that the maximum frequency is 20.
The modal class is, 40-50
Therefore, I=40,

f_{1} = 20

f_{2} = 11, f_{0} = 12

and h=10 .
So, the mode of the given data is,

\Rightarrow mode = 40 + (\frac{20 - 12}{2 (20) - 12 - 11}) 10

\Rightarrow mode = 40 + \frac{80}{17}

\Rightarrow \mod e = 40 + 4.7

\Rightarrow mode = 44.7

Therefore, the mode of the data is 44.7.
Hence, option 1 is the correct answer.

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