If the standard deviation of 0, 1, 2, 3, dots | vedclass

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(A) The standard deviation of a set of observations is independent of the change of origin.Let the first sequence be $x_i = \{0, 1, 2, \dots, 9\}$ wit

Vedclass · Accepted Answer

$K$

Vedclass · Answer

(A) The standard deviation of a set of observations is independent of the change of origin.Let the first sequence be $x_i = \{0, 1, 2, \dots, 9\}$ with standard deviation $K$.The second sequence is $y_i = \{10, 11, 12, \dots, 19\}$,which can be written as $y_i = x_i + 10$.Since the standard deviation is invariant under the addition of a constant to each observation,the standard deviation of $y_i$ is equal to the standard deviation of $x_i$.Therefore,the standard deviation of the second sequence is also $K$.

Class Interval	$0$-$4$	$4$-$8$	$8$-$12$	$12$-$16$	$16$-$20$
Frequency	$2$	$4$	$6$	$3$	$1$

If the standard deviation of $0, 1, 2, 3, \dots, 9$ is $K$,then the standard deviation of $10, 11, 12, 13, \dots, 19$ is

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