If the standard deviation of is , then the value of standard deviation of is

Question

If the standard deviation of $a_{1}, a_{2}, a_{3}, \dots, a_{2025}$ is $λ$ , then the value of standard deviation of $2 a_{1} - 1, 2 a_{2} - 1, 2 a_{3} - 1, \dots, 2 a_{2025} - 1$ is

Smart Achievers · Accepted Answer

(2)

As standard deviation is independent of change of origin

$∴$ It remains same $∴$ $S . D = 2 λ$

Solution

Q.
If the standard deviation of $a_{1}, a_{2}, a_{3}, \dots, a_{2025}$ is $λ$ , then the value of standard deviation of $2 a_{1} - 1, 2 a_{2} - 1, 2 a_{3} - 1, \dots, 2 a_{2025} - 1$ is

1 $3 λ$

2 $2 λ$

3 $λ - 1$

4 $2 λ + 1$

Ans.
(2)

As standard deviation is independent of change of origin

$∴$ It remains same $∴$ $S . D = 2 λ$

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Solution

Q. If the standard deviation of a1,a2,a3,…,a2025 is λ, then the value of standard deviation of 2a1-1,2a2-1,2a3-1,…,2a2025-1 is

1 3λ

2 2λ

3 λ-1

4 2λ+1

Ans. (2) As standard deviation is independent of change of origin ∴ It remains same ∴ S.D=2λ