Tag: shortcut method to find variance and standard deviation

Questions Related to shortcut method to find variance and standard deviation

Standard deviation is calculated from the Harmonic Mean (HM).

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Always

  2. Sometimes

  3. Never

  4. None of these

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Correct Option: C
Explanation:

Standard deviation is calculated from mean $i.e$ arithmetic mean.

It never be calculated from harmonic mean.

Lowest value of variance can be:

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $1$

  2. $-1$

  3. $0$

  4. None of these

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Correct Option: C
Explanation:
We know that $Var(x)=E(X^2)-(E(x))^2$

Variance is non-negative because the squares are positive or zero.

Therefore, $Var(X)\geq 0$

Hence, the lowest value of variance is $zero$

What is the standard deviation of $7,9,11,13,15$?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $2.4$

  2. $2.5$

  3. $2.7$

  4. $2.8$

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Correct Option: A
Explanation:

Given numbers are $ 7,9,11,13,15$
Mean of given numbers $=\dfrac { 7+9+11+13+15 }{ 5 } =11$
Standard deviation$=\dfrac { |7-11|+|9-11|+|11-11|+|13-11|+|15-11| }{ 5 } =2.4$
Option A is true

__________ is the positive square root of the mean of squared deviations from mean. 

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Mean Deviation

  2. Standard Deviation

  3. Quartile Deviation

  4. None of the above

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Correct Option: B

Which of the following are Methods of calculating Standard Deviation?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Actual Mean Method

  2. Assumed Mean Method

  3. Step-Deviation Method

  4. All of these

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Correct Option: D

Which of the following is true?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Standard Deviation is not affected by the value of the constant from which deviations are calculated.

  2. The value of the constant does not figure in the standard deviation formula

  3. Standard Deviation is Independent of Origin.

  4. All of these

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Correct Option: D

Which of the following represents median?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. First quartile

  2. Fiftieth percentile

  3. Sixth decile

  4. None of the above

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Correct Option: B

If the A.M of a set of observations is $9$ and its G.M is $6$. Then the H.M of the set of observations is ____.

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $4$

  2. $6$

  3. $3$

  4. None of them

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Correct Option: A

To find the median, it is necessary to arrange the data in _______.

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. ascending order

  2. descending order

  3. ascending or descending order

  4. any of them

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Correct Option: D

Calculate standard deviation of the following data.

X $0-10$ $10-20$ $20-30$ $30-40$ $40-50$
f $10$ $8$ $15$ $8$ $4$
business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $-12$

  2. $12$

  3. $12.36$

  4. $152.77$

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Correct Option: C
Explanation:
Marks Mid-values(X) f dxi$=X-25/10$ $fdx _if$ $dx _i^2$
$0-10$ $5$ $10$ $-2$ $-20$ $40$
$10-20$ $15$ $8$ $-1$ $-8$ $8$
$20-30$ $25$ $15$ $0$ $0$ $0$
$30-40$ $35$ $8$ $1$ $8$ $8$
$40-50$ $45$ $4$ $2$ $8$ $16$
Total $45$ $-12$ $72$

$\sqrt{\displaystyle\frac{72}{45}-\frac{144}{45\times 45}}\times 10$
$=12.36$