Standard Deviation

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New answer posted•a year ago

Standard Deviation Class 11th

Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

6 Views|Posted a year ago

Asked by Raj Pandey

Answered by

Raj Pandey | Contributor-Level 9

a year ago

Variance of a, b, c & a+2, b+2, c+2, are same.
Given: b = a + c (i)
d² = (1/3) (a² + b² + c²) - [ (a+b+c)/3]²
as a + c = b
d² = (1/3) (a² + b² + c²) - (2b/3)²
9d² = 3 (a² + b² + c²) - 4b²
⇒ b² = 3 (a² + c²) - 9d²

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New answer posted•a year ago

Standard Deviation Class 11th

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ and then reduced by $q$ , where $p = 0$ and $q \neq 0$ . If the new mean and new s.d. become half of their original values, then $q$ is equal to:

2 Views|Posted a year ago

Asked by Raj Pandey

Answered by

Raj Pandey | Contributor-Level 9

a year ago

If each observation is multiplied with p and then q is subtracted
New mean x? = px? - q ⇒ 10 = p(20)-q
and new standard deviations σ? = |p|σ? ⇒ 1 = |p|(2) ⇒ |p|=1/2 ⇒ p=±1/2
If p=1/2, then q=0. If p=-1/2, q=-20.

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New answer posted•a year ago

Standard Deviation Class 11th

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is

9 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

$\bar{x} = \frac{\sum_{i = 1}^{10} x_{i}}{10} = 15 \frac{\sum_{i = 1}^{10} {x_{i}}^{2}}{10} - {(\bar{x})}^{2} = 15$

$\Rightarrow Σ x_{i} = 150 Σ {x_{i}}^{2} = 2400$

Actual mean $\bar{x} = \frac{Σ x_{i} + 15 - 25}{10} = \frac{140}{10} = 14$

Actual variance = $\frac{Σ {x_{i}}^{2} + 1 5^{2} - 2 5^{2}}{10} - {(14)}^{2}$

$= \frac{2400 - 400}{10} - 196$

$\begin{array}{l} σ^{2} = 4 \\ σ = 2 \end{array}$

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Standard Deviation

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Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q , where p = 0 and q ≠ 0 . If the new mean and new s.d. become half of their original values, then q is equal to:

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ and then reduced by $q$ , where $p = 0$ and $q \neq 0$ . If the new mean and new s.d. become half of their original values, then $q$ is equal to: