Correct option is D
Given:
If the standard deviation of a dataset is zero, it means:
All values in the dataset are exactly equal.
This is because standard deviation measures how much the numbers deviate from the mean.
If there is no deviation, then every number is identical.
Solution:
Since all five numbers are the same, the following must be true:
- Mean = Median = Mode = the common value
- The difference between median and mode = 0
Let’s evaluate the options:
Option A: All the numbers are zero
→ Not necessarily true.
They could all be 5, or -3, or any identical value.
Incorrect
Option B: The median is zero
→ Not necessarily true.
Median = the middle value, which is equal to all others, but need not be zero.
Incorrect
Option C: If at least one number is positive, then at least one number is negative
→ No, if one number is positive, all are positive (since all values are equal).
Incorrect
Option D: The difference between the median and mode of these numbers is zero
→ Correct, since all values are equal, median = mode
=> Difference = 0
Correct
Final Answer:
S. Ans. (D) The difference between the median and mode of these numbers is zero
