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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 – $\dpi{100} \mu$)2 ] / N, where i = 1,2, …, N ,                    xi are observations,  $\dpi{100} \mu$ is mean, N is number of observations.Solving this we get variance = [∑xi2 – N$\dpi{100} \mu$2] / N  =  (∑xi2 / N) – $\dpi{100} \mu$2 and standard deviation is square root of variance.Initial mean ($\dpi{100} \mu$1) = 25 = ∑xi / 8  Initial standard deviation ($\dpi{100} \sigma$) = 5  $\dpi{100} \Rightarrow$  Initial variance ($\dpi{100} \sigma$2) = 52 = 25 = (∑xi2 / 8) – $\dpi{100} \mu$12 $\dpi{100} \therefore$  25 = (∑xi2 / 8) – 252   or   (∑xi2 / 8) = 25 + 625 = 650∑xi2 = 650 x 8 = 5200. Now, finally there are 10 items. Final mean, $\dpi{100} \mu$2  = ($\dpi{100} \mu$1 x 8 + 15 + 25) / 10 = (25 x 8 +15 + 25) / 10 = 240 / 10  =  24.Final variance = (final ∑xi2 / final N) – $\dpi{100} \mu$2 2  =  {(5200 + 152 + 252) / 10} – 242                        =  {(5200 + 225 + 625) / 10} – 576                       =  605 – 576                       =  29.

one month ago
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