Question

The following table shows the number of students sorted according to marks in Maths exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ 30-40& 3\\ 40-50& 5\\ 50-60& 8\\ 60-70& 11\\ 70-80& 14\end{array}$

Find the Approximate Median Marks obtained by the students.

• A. 62.57
• B. 68.2
• C. 64.09
• D. 57.6

Answer 1

The correct option is C

64.09

The cumulative frequency table can be given as :

$\begin{array}{cc}\text{Marks}& \text{No. of students(Cumulative)}\\ <40& 3\\ <50& 8\\ <60& 16\\ <70& 27\\ <80& 41\end{array}$

N = 41 (An odd number)

Median = $\frac{(41+1)}{2}th$ observation = 21st observation.

So, the Median class is 60 - 70

We know that there are 11 students from the 16th student to the 27th student who score between 60 and 70.

However, we do not know their individual marks.

We will divide 10 from 60 to 70 into 11 equal parts and assume that one observation is in each subdivision.

We will assume that the value of each observation in a subdivision is the mid - value of the subdivision.

So, the the value of the 17th student is the mid value of 60 and $60\frac{10}{11}$ft, that is $60\frac{10}{22}$

So, from the 17th student to the 21st student, there are 4 observations.

If the 17th term of the AP is $60\frac{10}{22}$ and the common difference is $\frac{10}{11}$,

Then the 21st term = $60\frac{10}{22}$ + $4\times \frac{10}{11}$

= $60+\frac{10+80}{22}$

= 60 + 4.09

= 64.09