Grade 12Trigonometry

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

Mahesh

7 Years agoGrade 12

1 Answer

Samyak Jain

7 Years ago

Ans. is 8.

We know that formula of variance is [∑(x_i – $\mu$ )² ] / N, where i = 1,2, …, N ,

x_i are observations, $\mu$ is mean, N is number of observations.

Solving this we get variance = [∑x_i² – N $\mu$ ²] / N = (∑x_i² / N) – $\mu$ ² and standard deviation is square root of variance.

Initial mean ( $\mu$ ₁) = 25 = ∑x_i / 8

Initial standard deviation ( $\sigma$ ) = 5 $\Rightarrow$ Initial variance ( $\sigma$ ²) = 5² = 25 = (∑x_i² / 8) – $\mu$ ₁²

$\therefore$ 25 = (∑x_i² / 8) – 25² or (∑x_i² / 8) = 25 + 625 = 650

∑x_i² = 650 x 8 = 5200.

Now, finally there are 10 items.

Final mean, $\mu$ ₂ = ( $\mu$ ₁ x 8 + 15 + 25) / 10 = (25 x 8 +15 + 25) / 10 = 240 / 10 = 24.

Final variance = (final ∑x_i² / final N) – $\mu$ ₂² = {(5200 + 15² + 25²) / 10} – 24²

= {(5200 + 225 + 625) / 10} – 576

= 605 – 576

= 29.

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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

Mahesh

1 Answer

Samyak Jain

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