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A student noted that the number of cars passing through a particular spot on the road for $200$ periods each of $10$ minutes and summarized in a table given below. What is the mode of the data?

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34.71

36.47

42.63

47.26

answer is A.

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Detailed Solution

It is given the number of cars passing through a particular spot on the road for

200

periods each of

10

minutes.

We know that,
Mode

= l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h

Where:

l \to

lower limit of the modal class

f \to

frequency of the modal class

f_{1} \to

frequency of the class preceding the modal class

f_{2} \to

frequency of the class succeeding the modal class

h \to

class width
from the given table, we get that the maximum frequency is

21

and the corresponding class is

30 - 40

. Therefore,

30 - 40

is the modal class.
According to the situation,

l = 30, h = 10, f = 21, f_{1} = 13

and

f_{2} = 12

Putting the values in the formula, we get

Mode = 30 + \frac{21 - 13}{42 - 13 - 12} \times 10

\Rightarrow Mode = 30 + \frac{8}{17} \times 10

\Rightarrow Mode = 30 + \frac{80}{17}

\Rightarrow Mode = 30 + 4.71

\Rightarrow Mode = 34.71

Therefore, the mode of the given frequency distribution is

34.71

.
Hence, the correct option is 1.

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