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13.Statistics
medium
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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