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Grade: 12
        
the mean and the standard deviation of a data of 8 items are 25 and 5 respectively. If two items 15 and 25 are added to this data, then the variance of the new data is
 
2 months ago

Answers : (1)

Samyak Jain
326 Points
							
Ans. is 8.
We know that formula of variance is [∑(xi – \mu)2 ] / N, where i = 1,2, …, N , 
                   xi are observations,  \mu is mean, N is number of observations.
Solving this we get variance = [∑xi2 – N\mu2] / N  =  (∑xi2 / N) – \mu2 and standard deviation is square root of variance.
Initial mean (\mu1) = 25 = ∑xi / 8  
Initial standard deviation (\sigma) = 5  \Rightarrow  Initial variance (\sigma2) = 52 = 25 = (∑xi2 / 8) – \mu12 
\therefore  25 = (∑xi2 / 8) – 252   or   (∑xi2 / 8) = 25 + 625 = 650
∑xi2 = 650 x 8 = 5200.
 
Now, finally there are 10 items. 
Final mean, \mu2  = (\mu1 x 8 + 15 + 25) / 10 = (25 x 8 +15 + 25) / 10 = 240 / 10  =  24.
Final variance = (final ∑xi2 / final N) – \mu2  =  {(5200 + 152 + 252) / 10} – 242 
                       =  {(5200 + 225 + 625) / 10} – 576
                       =  605 – 576
                       =  29.
one month ago
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