Question

In a continuous frequency distribution, median of the data is24. If each

observation is increased by 2, then the new median will be

a. 24 b. 26 c. 12 d. 48​

Answer 1

Answer:

if each of the data is increased by 2 then the new median will also increased by 2

Answer 2

The new median will be 26.

Option B is correct.

Given:

• In a continuous frequency distribution, the median of the data is 24.
• If each observation is increased by 2.

To find:

• The new median will be
• a. 24
• b. 26
• c. 12
• d. 48

Solution:

Concept to be used:

1. Arrange the numbers in the ascending order.
2. If n is odd, then $\left( \frac{n + 1}{2}\right )^{th}$term.
3. If n is even,then median is mean of $\left (\frac{n}{2}\right) ^{th} \: and \: \left(\frac{n}{2} + 1 \right)^{th}$ terms.

ATQ,

The median of continuous distribution of data is 24.

If total numbers are odd then the median is the middle data, i.e. $\left( \frac{n + 1}{2}\right )^{th}$term.

ATQ,

Every observation is increased by 2, then the middle number will also be increased by 2, so the median new will be 26.

If total observations are even, then the median of observations are mean of two terms.

We know that, if every observation is increased by 2 then the mean will be increased by 2, so the median of data will be increased by 2.

Thus,

In both the cases (n; Even or Odd) the median will be increased by 2.

Thus,

The new median will be 26.

Option B is correct.

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