Consider a dataset A with 55 observations, all distinct. Dataset D is created from A by adding 2023 to the largest observation in A and subtracting 2023 from the smallest observation in A. Which of the following is NOT true?

Correct option is D

Solution:

1. Mean of D = Mean of A?
Mean = (Sum of values) ÷ (Number of values)
Adding 2023 to one number

Subtracting 2023 from another

So the total sum remains unchanged

Number of values = 55 (same in both A and D)

Conclusion: Mean of D equals Mean of A → True

2. Sum of D = Sum of A?
One value is increased by 2023

Another is decreased by 2023

So the net effect on the sum is 0

Conclusion: Sum of D equals Sum of A → True

3. Median of D = Median of A?
The median is the middle value when sorted

Since only the smallest and largest values change, and they are at the ends of the list, the middle (28th) value remains the same

Conclusion: Median remains unchanged → True

4. Standard Deviation of D = Standard Deviation of A?
This is the critical point.

Standard deviation measures the spread of data from the mean

In dataset D:

The maximum value becomes larger

The minimum value becomes smaller

So now the spread is wider

Since the values are further away from the mean, the standard deviation increases

Conclusion: Standard deviation of D is greater than that of A → This is NOT true

Final Answer:
S. Ans. (d) Standard deviation of D = Standard deviation of A