Question

For the following distribution:

Marks	Below 10	Below 20	Below 30	Below 40	Below 50	Below 60
No. of students	3	12	27	57	75	80

Find the median class.

Answer 1

Hint:
Here we will first convert the given data which is in less than type into the normal form of the class of data by subtracting the frequency of that class with the preceding class frequency. Then we will find the value of half the total frequency. Then, we will check in which class in which the value of half the total frequency lies to find the required median class.

Complete Step by Step Solution:
First, we will convert the given data into normal data form as the data is given in less than type form.
So to convert the data from less than type data to the normal data we will subtract the frequency of that class with the preceding class frequency. Therefore, we get

Marks class	No. of students
0-10	3
10-20	\[12 - 3 = 9\]
20-30	\[27 - 12 = 15\]
30-40	\[57 - 27 = 30\]
40-50	\[75 - 57 = 18\]
50-60	\[80 - 75 = 5\]

Now we know that the value of the total frequency is equal to 80 i.e. \[n = 80\].
Now we will find the value of \[\dfrac{n}{2}\] and check in which class it lies in. Therefore, we get
\[\therefore \dfrac{n}{2}=\dfrac{80}{2}=40\]
40 lies in the class of 30-40 as till class 20-30 only 27 students are there. So, the median class will be 30-40.

Hence class 30-40 is the median class of the data.

Note:
Here, we should not get confused between mean, median, and mode. Median is the middle value of the given list of numbers or it is the value that is separating the data into two halves i.e. upper half and lower half. A mode is a number or value which occurs a maximum number of times in a given set of numbers. Mean is the average of the given data.