The standard deviation of 20 observations is√5 If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.
σ =√5 , n = 20
Therefore, new S.D. = σ = √5×2=2√5
∴ The new variance = σ2 = 4 × 5 = 20.
If the mean and standard deviation of 75 observations is 40 and 8 respectively, find the new mean and standard deviation if
(i) Each observation is multiplied by 5.
(ii) 7 is added to each observation.
The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.