Tag: shortcut method to find variance and standard deviation

Questions Related to shortcut method to find variance and standard deviation

For a distribution, coefficient of variation is 22.5% and mean is 7.5 find the 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. 1.9975

  2. 1.6875

  3. 1.243

  4. 1.0943

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Correct Option: B

In a class of 100, the mean on a certain exam was 50, the standard deviation, 0. This means..........................

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. half the class had scores less than 50

  2. there was a high correlation between ability and grade

  3. everyone had a score of exactly 50

  4. half the class had 0's and half had 50's

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Correct Option: C
Explanation:

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. If standard deviation of a certain series is zero than it denotes that all the values of that series is equal to the mean of the series which made all the deviations zero and therefore standard deviation also zero. 

Average Marks of a group of $50$ students appeared in CA CPT exams is $134$ marks. If $10\%$ students scored more than $137$ marks, find the standard deviation of marks_____.

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. $1.98$

  2. $2.336$

  3. $3.05$

  4. $2.98$

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Correct Option: B

If a population has a standard deviation of $2.25$, how large the sample should be to allow a maximum error of $0.33$ with $95\%$ confidence level?

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. $252$

  2. $201$

  3. $220$

  4. $178$

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Correct Option: D

The standard deviation $\sigma$ of the first $N$ natural numbers can be obtained using which one of the following formula?

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. $\sigma =\cfrac { { N }^{ 2 }-1 }{ 12 } $

  2. $\sigma =\sqrt { \cfrac { { N }^{ 2 }-1 }{ 12 } } $

  3. $\sigma =\sqrt { \cfrac { N-1 }{ 12 } } $

  4. $\sigma =\sqrt { \cfrac { { N }^{ 2 }-1 }{ 6N } } $

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Correct Option: C
Explanation:

$\sigma^2=\dfrac{1}{n}\sum _{i=1}^{n}i^2-\left(\dfrac{1}{n}\sum _{i=1}^{n}i\right)^2$


     $=\dfrac{1}{n}(1^2+2^2+...+n^2)-\left(\dfrac{1}{n}(1+2+...+n)\right)^2$

     $=\dfrac{1}{n} \times \dfrac{n(n+1)(2n+1)}{6}-(\dfrac{n+1}{2})^2=\dfrac{n^2-1}{12}$

$\therefore \sigma=\sqrt{\dfrac{n^2-1}{12}}$

A researcher has collected the following sample data. The mean of the sample is 5.
3  5  12  3  2
The standard deviation 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. 8.944

  2. 4.062

  3. 13.2

  4. 16.5

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Correct Option: B