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# A student noted the number of cars passing through the spot on the road for 200 periods each of 10 minutes and summarized in the table given below. Find the mode of the dataNumber of cars0-1010-2020-3030-4040-5050-6060-7070-80Frequency7913211215412

Last updated date: 13th Jun 2024
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Hint: Here we have to find the mode of the following frequency data. For that, we will first find the modal class. Then we will find the lower limit of the modal class, frequency of the modal class, frequency of the class before the modal class, frequency of the class after the modal class. Then we will find the size of the class interval. We will put all the data in the formula of mode.

Formula Used:
We will use the formula of the mode which is given by
$Mode = l + \dfrac{{f - {f_1}}}{{2f - {f_1} - {f_2}}} \times h$ , where, $l$ is the lower limit of modal class, $h$ is the size of the class intervals, $f$ is the modal class, ${f_1}$ is the frequency of the class preceding the modal class, ${f_2}$ is the frequency of the class succeeded in the modal class.

Here the modal class is $30 - 40$ .
$\begin{array}{l}l = 30\\f = 21\\{f_1} = 13\\{f_2} = 12\\h = 10\end{array}$
Now, we will substitute all the values in the formula of mode, $mode = l + \dfrac{{f - {f_1}}}{{2f - {f_1} - {f_2}}} \times h$.
$\Rightarrow {\rm{mode}} = 30 + \dfrac{{21 - 13}}{{2 \times 21 - 13 - 12}} \times 10$
$\Rightarrow {\rm{mode}} = 30 + \dfrac{8}{{17}} \times 10$
$\Rightarrow {\rm{mode}} = 34.705$