Statistics
Statistics
nta_abhyas_2025
Grade 11
Question:
If the standard deviation of 0, 1, 2, $\ldots$, 9 is $k$, then the standard deviation of 10, 11, 12, $\ldots$, 19 is
Step-by-Step Solution
Key Concept: Standard deviation and variance are invariant under translation (change of origin) of data
Here, we see that 10 is added to each observation of the first data. Since we know that standard deviation does not depend on change of origin (adding or subtracting a constant from each observation does not change the standard deviation), the variance remains unchanged. Therefore, both datasets have the same variance.
Correct Answer: 4