7.Consider the following data as a sample.
15, 15, 33, 17, 30, 30, 20, 60, 45, 15
If each data value is increased by 5, what is the effect on the mean and
standard deviation?
Both the mean and the standard deviation increase by 5.
The mean remains the same, but the standard deviation increases by 5.
The standard deviation remains the same, but the mean increases
by 5.
Both the mean and the standard deviation remain the same

The correct answer is: The standard deviation remains the same, but the mean increases by 5.​

Dataset Calculations

For the sample data 15, 15, 33, 17, 30, 30, 20, 60, 45, 15, the original mean is 28.0, calculated as the sum (280) divided by 10 observations. The population standard deviation is approximately 14.28, derived from the square root of the average squared deviations from the mean. After adding 5 to each value (new data: 20, 20, 38, 22, 35, 35, 25, 65, 50, 20), the new mean becomes 33.0, exactly 5 units higher, while the standard deviation stays 14.28.​

Adding a constant $k$ (here, $k=5$) to every data point shifts the mean by $k$, so new mean xˉ′=xˉ+kxˉ′=xˉ+k. Standard deviation measures spread around the mean via deviations (xi−xˉ)(xi−xˉ); adding $k$ to each xixi and xˉxˉ leaves deviations unchanged, so σ′=σσ′=σ.​

Option Analysis

• Both the mean and the standard deviation increase by 5: Incorrect, as standard deviation depends on relative differences, not absolute shifts.​

• The mean remains the same, but the standard deviation increases by 5: Incorrect; mean shifts by the constant added.​

• The standard deviation remains the same, but the mean increases by 5: Correct, matching the calculation and statistical properties.​

• Both the mean and the standard deviation remain the same: Incorrect; only standard deviation (and variance) is invariant to location shifts.​

This concept appears in CSIR NET Life Sciences quantitative aptitude sections, testing understanding of descriptive statistics transformations.​​