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

Moderate

A

-7
B

-4
C

7
D

1.75

Solution

We know that if $d_{i} = \frac{x_{i} - A_{1}}{h} .$ then $σ_{x} = | h | σ_{d}$
In this case $- 2 x_{i} - 3 =∣ \frac{x_{i} + 3 / 2}{- 1 / 2}$ so $h =\leftarrow - 1 / 2 .$ Thus $σ_{d} =$
$\frac{1}{| h |} σ_{x} = - 2 \times 3.5 = - 7$ .

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