Question

Find the median class of the following data:

Number of cars	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	7	9	13	21	12	15	4	12

A. 30-40
B. 40-50
C. 50-60
D. 60-70

Answer 1

Hint: To find the median class of the given data, we will find the cumulative frequency by adding the frequency in the current step with the cumulative frequency found in the previous step. Next find the sum of frequencies denoted by $\sum{f}$ . Next, we have to find $\dfrac{\sum{f}}{2}$ and check the cumulative frequency which is nearest to or greater than this value. The corresponding class will be the median class.

Complete step-by-step answer:
We need to find the median class of the given data. We can do this by finding the cumulative frequency. This is shown below:

Number of cars	Frequency	Cumulative frequency (cf)
0-10	7	7
10-20	9	$9+7=16$
20-30	13	$13+16=29$
30-40	21	$21+29=50$
40-50	12	$12+50=62$
50-60	15	$15+62=77$
60-70	4	$4+77=81$
70-80	12	$12+81=93$

We can find cumulative frequency by adding the frequency in the current step with the cumulative frequency found in the previous step.
Now, let us find $\sum{f}$ or the sum of frequencies. We can find this by adding the frequencies or this is same as the cumulative frequency in the last column.
Hence, \[\sum{f}=93\] .
Now, we have to find $\dfrac{\sum{f}}{2}$ . That is,
$\dfrac{\sum{f}}{2}=\dfrac{93}{2}=46.5$
Now, we have to check the cumulative frequency which is nearest to or greater than 46.5. From the table. We can see the cumulative frequency=50. Hence, the median class will be 30-40.

So, the correct answer is “Option B”.

Note: When finding cumulative frequency, you may add the frequency of the previous class and the current class frequency. This will lead to wrong results.We have to add the current class frequency with previous cumulative frequency. When checking the corresponding median class of $\dfrac{\sum{f}}{2}$ value, do not check in the frequency column. You have to check in the cumulative frequency column.