Question

If the standard deviation of \( 0,1,2,3,\ldots,9 \) is \( k \), then the standard deviation of \( 10,11,12,13,\ldots,19 \) will be:

• A. \( k + 4 \)
• B. \( k + 10 \)
• C. \( k \)
• D. \( k + 8 \)

Hint:

Adding or subtracting a constant shifts data but does not affect standard deviationOnly multiplication or division changes it.

Answer 1

The Correct Option is C

Step 1: Understand the datasets.
First dataset:
\[ 0,1,2,3,\ldots,9 \]
Second dataset:
\[ 10,11,12,13,\ldots,19 \]
We observe that each element of the second dataset is obtained by adding \( 10 \) to the first dataset.

Step 2: Property of standard deviation.
If a constant \( a \) is added to every observation, then:
\[ \text{Standard deviation remains unchanged} \]
Because standard deviation measures spread, not location.

Step 3: Apply the property.
Second dataset = First dataset \( + 10 \)
Hence, their standard deviations are equal.

Step 4: Final conclusion.
\[ \boxed{\text{Standard deviation} = k} \]