If standard deviation of 0, 1, 2, 3, …..,9 is K , then standard deviation of 10, 11, 12, 13 &

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

A

$K$

B

$K + 10$

C

$K + \sqrt {10} $

D

$10\ K$

Solution

As the standard deviation only depend upon total no of values and the difference between mean and each value,

Both sequence have same standard deviation.

Note:

If $1^{\text {st }}$ sequence is $x _{ i }$ and $2^{\text {nd }}$ sequence is $y _{ i }$,

$y _{ i }=10+ x _{ i } \Rightarrow \overline{ y }=10+\overline{ x }$

So, $\overline{ y }- y _{ i }=\overline{ x }- x _{ i }$

Standard 11

Mathematics

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