JEE Mathematics 2024 Question with Solution

Given: The grouped frequency distribution has classes $0-4, 4-8, 8-12, 12-16, 16-20$ with frequencies $3, 9, 10, 8, 6$.

Find: The value of $20M$, where $M$ is the median.

First, calculate the cumulative frequency:

• For $0-4$: $3$
• For $4-8$: $3+9=12$
• For $8-12$: $12+10=22$
• For $12-16$: $22+8=30$
• For $16-20$: $30+6=36$

The total frequency is

so

The median class is $8-12$, because its cumulative frequency $22$ is the first one that exceeds $18$.

Now use the median formula:

Here,

• $l=8$
• $f=10$
• $C=12$
• $h=4$

Substituting these values:

Then,

Therefore, the value of $20M$ is $208$. The correct option is D.

Given: A grouped frequency distribution is provided.

Find: Median $M$ and then compute $20M$.

For grouped data, the median is found from the class containing **$\frac{N}{2}$**th observation.

Compute total frequency:

Hence,

Construct cumulative frequencies:

Since $18$ lies between $12$ and $22$, the median class is $8-12$.

Thus,

• lower limit $l=8$
• preceding cumulative frequency $c.f.=12$
• median class frequency $f=10$
• class width $h=4$

Apply the formula:

Finally,

So, the correct answer is D.