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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is:

(a) 50000

(b) 250000

(c) 252500

(d) 255000

4 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} H e r e \bar{x} = \frac{\sum_{}^{} x_{i}}{n} \\ 50 = \frac{\sum_{}^{} x_{i}}{100} \Rightarrow \sum_{}^{} x_{i} = 5000 \\ ∴ S . D . = \sqrt[]{\frac{\sum_{}^{} x_{i}^{2}}{n} - {(\frac{\sum_{}^{} x_{i}}{n})}^{2}} \\ 5 = \sqrt[]{\frac{\sum_{}^{} x_{i}^{2}}{100} - {(\frac{5000}{100})}^{2}} \Rightarrow 25 = \frac{\sum_{}^{} x_{i}^{2}}{100} - 2500 \\ \Rightarrow \frac{\sum_{}^{} x_{i}^{2}}{100} = 2500 + 25 \Rightarrow \frac{\sum_{}^{} x_{i}^{2}}{100} = 2525 \\ ∴ \sum_{}^{} x_{i}^{2} = 2525 \times 100 = 252500 \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

Let $x_{1}, x_{2}, \dots, x_{n}$ be $n$ observations and $\overset{?}{x}$ be their arithmetic mean. The formula for the standard deviation is given by:

(a) $\frac{1}{n} \sum_{i = 1} {(x_{i} - \overset{?}{x})}^{2}$

(b) $\frac{1}{n} \sum_{i = 1} {(x_{i} - \overset{?}{x})}^{2}$

(c) $\frac{\sum^{n} x_{i}^{2}}{n} - {\overset{?}{x}}^{2}$

(d) $\sum_{i = 1} x_{i}^{2} + n {\overset{?}{x}}^{2}$

4 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e f o r m u l a f o r S . D . = σ = \sqrt[]{\frac{\sum_{}^{} {(x_{i} - \bar{x})}^{2}}{n}} \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

The standard deviation is ________to the mean deviation taken from the arithmetic mean.

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Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e s t a n d a r d d e v i a t i o n s i s g r e a t e r t h a n o r e q u a l t o t h e m e a n d e v i a t i o n t a k e n f r o m t h e \\ a r i t h m e t i c m e a n . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s g r e a t e r t h a n o r e q u a l . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

The mean deviation of the data is ________ when measured from the median.

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e m e a n d e v i a t i o n o f t h e d a t a i s l e a s t w h e n m e a s u r e d f r o m t h e m e d i a n . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s l e a s t . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

The sum of the squares of the deviations of the values of the variable is ________when taken about their arithmetic mean.

6 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e s u m o f t h e s q u a r e s o f t h e d e v i a t i o n s o f t h e v a l u e o f i s minimum w h e n t a k e n \\ a b o u t t h e i r a r i t h m e t i c m e a n . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s minimum \end{array}$ $\begin{array}{l} \end{array}$ $\begin{array}{l} . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

The standard deviation of a data is of any change in origin but is on the change of scale.

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Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} Since t h e standard d e v i a t i o n o f a n y d a t a i s i n d e p e n d e n t o f a n y c h a n g e i n o r i g i n b u t i s \\ d e p e n d e n t o f a n y c h a n g e o f s c a l e . \\ H e n c e, t h e v a l u e o f t h e f i l l e r a r e i n d e p e n d e n t a n d d e p e n d e n t . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

If the variance of a data is 121, then the standard deviation of the data is ________

4 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$W e k n o w t h a t S D =$ =√variance= $\begin{array}{l} \sqrt[]{121} = 11 \end{array}$

$\begin{array}{l} H e n c e, t h e v a l u e o f t h e f i l l e r i s 11 . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

If $\bar{x}$ is the mean of $n$ values of $x$ , then $\sum_{i = 1} (x_{i} - \overset{?}{x}) .$ equal to ________. If $a$ has any value other than $\overset{?}{x}$ , then $\sum_{i = 1} {(x_{i} - a)}^{2}$ is_______than ${(x_{i} - a)}^{2}$

4 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} I f \bar{x} i s t h e m e a n o f n o b s e r v a t i o n s o f x, t h e n \sum_{i = 1}^{n} x_{i} - \bar{x} = 0 a n d i f' a' h a s t h e v a l u e o t h e r \\ t h a n \bar{x}, t h e n \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} i s l e s s t h a n t h a n \sum_{}^{} {(x_{i} - a)}^{2} . \\ H e n c e, t h e v a l u e o f t h e f i l l e r a r e 0 a n d l e s s . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fifteen

Coefficient of variation = ./mean × 100.

3 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n t h a t σ_{C} = 5 \\ C V = \frac{S D}{M e a n} \times 100 \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s S D . \end{array}$