The mean of 100 observations is 50 and the standard deviation is 10 . If 5 is subtracted from each observation and then it is divided by 4 , then what will be the new mean and the new standard deviation respectively?

Step-by-step solution

Number of observations ( N )=100 Mean ( x )=50 Standard deviation ( )=10 New mean, x _ I = x-5 4 N = 1 4 ( x N -5 )= 1 4 (50-5)= 45 4 =11.25 New standard deviation ( ₁ )= ( x-5 4 )= 1 4 (x-5)= 1 4 (x)= 10 4 =2.5