Question

if S is the standard deviation of values p q r then the standard deviation of P - 3 q- 3 and r- 3 is​

Answer 1

Given : S is the standard deviation of values p q r

To Find : standard deviation of P - 3 q- 3 and r- 3

Solution:

Standard Deviation   = √ ∑(xi - mean)² / n

S is the standard deviation of values p q r

standard deviation of p - 3 q- 3 and r- 3   will also be S

Let say mean of p , q  r  = m  

m = (p + q + r)/3

then S  =  √[{ (p - m)² + (q - m)²  + (r - m)²} / 3]

p - 3 q- 3 and r- 3  

Mean = ( p - 3 + q - 3 + r - 3) /3 = (p + q + r)/3  - 3

=  m - 3  

SD = √[{ (p -3 - (m-3))² + (q-3 - (m-3))²  + (r -3  - (m-3))²} / 3]

=  √[{ (p - m)² + (q - m)²  + (r - m)²} / 3]

= S

Hence standard deviation of p - 3 q- 3 and r- 3   will also be S

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