Question

The mean of 6 numbers is 15, and the standard deviation is 2. If each number is increased by 5, what is the new standard deviation?

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

Adding a constant to all data points shifts the mean but does not affect the standard deviation, as it measures relative spread.

Answer 1

The Correct Option is A

The standard deviation measures the spread of data, which is unaffected by a constant shift. If each number is increased by 5, the mean changes, but the standard deviation remains the same. Given the original standard deviation is 2: \[ \text{New standard deviation} = 2 \] To confirm, recall that standard deviation is calculated as: \[ \sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}} \] If each \( x_i \) is increased by 5, the new values are \( x_i + 5 \), and the new mean is \( \bar{x} + 5 = 15 + 5 = 20 \). The deviations become: \[ (x_i + 5) - (\bar{x} + 5) = x_i - \bar{x} \] Thus, the standard deviation remains unchanged. The new standard deviation is: \[ \boxed{2} \]