First slide

Introduction to statistics

Question

If the standard deviation of $x_{1}, x_{2}, \dots, x_{n} is 3 .5$ , then the standard deviation of $- 2 x_{1} - 3, - 2 x_{2} - 3, \dots - 2 x_{n} - 3$ is

Easy

A

-7
B

-4
C

7
D

1.75

Solution

If $d_{i} = \frac{x_{i} - A}{h}$ then, $σ_{x} = | h | σ_{d}$
$\begin{array}{l} Now, - 2 x_{i} - 3 = \frac{x_{i} + \frac{3}{2}}{- \frac{1}{2}} \\ Here, h = - \frac{1}{2} \\ σ_{d} = \frac{1}{| h |} σ_{x} = 2 \times 3 .5 = 7 \end{array}$

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