Q5 of 108 Page 32

The mean and standard deviation of 6 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.

Given, The mean is 8 and SD is 4 for 6 observation

To Find: Find a new mean and new standard Deviation.


Formula Used: Standard Deviation ()


Explanation:


Let Assume, x1,x2,x3,…,x6 be the given observations.


So, Variance (X) = 8 (Given)


n=6


and (SD)


X =



Now, Let u1,u2,…u20 be the new observation,


When we multiply the new observation by 3, then


Ui=3xi (for i=1,2,3…,6) ……(i)


Now,






3×8 = 25


U = 24


Therefore, The Mean of new observation is 24


Now,


Standard Deviation



Since, Variance (X) =16


Variance (U) =



9×16





Hence, The mean of new observation is 24 and Standard deviation of new data is 12.


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