NDA 2026 — Mathematics PYQ

To find the new standard deviation, we use the scaling property of standard deviation when observations are multiplied by a constant.

1. Understand the Mathematical Property

When every observation $x_i$ in a dataset is multiplied by a constant factor $k$, the new standard deviation ${\sigma }_{new}$ is the absolute value of $k$ multiplied by the original standard deviation ${\sigma }_{old}$.

$${\sigma }_{new}=|k|\cdot {\sigma }_{old}$$

2. Calculation

Given the data from image_d1d1bf.png:

• The original standard deviation ${\sigma }_{old}=10$.

• The multiplication factor $k=5$.

Substituting these values into the formula:

$${\sigma }_{new}=5\times 10$$

$${\sigma }_{new}=50$$

Correct Option:

(d) 50