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Question
Let x1, x2, x3, x4, x5 be the observations with mean m and standard deviation s. The standard deviation of the observations kx1, kx2, kx3, kx4, kx5 is ______.
Options
k + s
`s/k`
ks
s
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Solution
Let x1, x2, x3, x4, x5 be the observations with mean m and standard deviation s. The standard deviation of the observations kx1, kx2, kx3, kx4, kx5 is ks.
Explanation:
Here m = `(sumx_i)/n`
s = `sqrt((sumx_i^2)/5 - ((sumx_i)/5)^2`
∴ S.D. = `sqrt((k^2sumx_i^2)/5 - ((ksumx_i)/5)^2`
= `sqrt((k^2sumx_i^2)/5 - k^2 ((sumx_i)/5)^2`
= `ksqrt((sumx_i^2)/5 - ((sumx_i)/5)^2`
= ks
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