Tag: shortcut method to find variance and standard deviation

Questions Related to shortcut method to find variance and standard deviation

Given mean = $70.2$ and mode = $70.5$, find median using empirical relationship among them.

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. $70.3$

  2. $70.5$

  3. $70.6$

  4. $70.4$

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Correct Option: A

Which measure of dispersion ensures highest degree of reliability?

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. Range

  2. Mean deviation

  3. Standard deviation

  4. Quartile deviation

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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. It is considered as the best and most commonly used measure of dispersion to ensure high degree of reliability as it is a measure of average of deviations from the average.

If each observation of set is divided by $10$, the S.D of the new 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. $10$ times of S.D of original obs.

  2. $\frac{1}{100}$th

  3. Not changed

  4. $\frac{1}{10}$th

Show answer
Correct Option: D
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. So the deviations are affected by division and multiplication. Therefore, if each observation of the set id divided by 10 then the whole standard deviation also becomes 1/10 th of the prior standard deviation. 

Which measure of dispersion has a different unit other than the unit of measurement of values?

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. Range

  2. Mean deviation

  3. Standard deviation

  4. Variance

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Correct Option: D
Explanation:
Variance is the mean of the squares of the deviations from the mean. Variance is the square of standard deviation. Therefore any unit of a given set is converted into squares at the time of calculating the variance.

A set of values is said to be relatively uniform if it has ________.

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. high dispersion

  2. zero dispersion

  3. little dispersion

  4. negative dispersion

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Correct Option: C
Explanation:

A set of values from an observation is said to be relatively uniform if all the observations of the series have very little dispersion from each other. 

If each value of a set is divided by a constant 'd', the co-efficient of variation will 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. more than original value

  2. less than original value

  3. same as original value

  4. none of the above

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Correct Option: C
Explanation:

Variance is the mean of the squares of the deviations from the mean. Variance is not affected by the addition, subtraction, multiplication and division of the given value. Therefore, if each value of the series is multiplied by 15, the coefficient of variation will be unaltered.

The C.V of a distribution is $80\%$ and the mean of the distribution is $40$, the S.D of the distribution 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. $33$

  2. $32$

  3. $35$

  4. $0.30$

Show answer
Correct Option: B
Explanation:

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.

Coefficient of variation = ( standard deviation / mean )

=> 80 /100 = S.D / 40 

=> S.D = 32 

If each value of a series is multiplied by a constant, the coefficient of variation as compared to original value 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. increased

  2. unaltered

  3. decreased

  4. zero

Show answer
Correct Option: B
Explanation:

Variance is the mean of the squares of the deviations from the mean. Variance is not affected by the addition, subtraction, multiplication and division of the given value. Therefore, if each value of the series is multiplied by 15, the coefficient of variation will be unaltered.

The standard deviation of $5$ items is found to be $15$. What will be the standard deviation if the values of all the items are increased?

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. $15$

  2. $20$

  3. $10$

  4. None of the above

Show answer
Correct Option: A
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. Standard deviation is not affected by the increase of decrease of observations in the series. 

The mean of $100$ observations is $18.4$ and sum of squares of deviations from mean is $1444$, the Co-efficient of variation 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. $30.6$

  2. $35.6$

  3. $20.6$

  4. $10.6$

Show answer
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.

Standard deviation = { (sum of the squares of the observations/ number of observations ) – (sum of observations/ number of observations ) } ½

                               = { (1444) –(18.4) } ½

                                = (1425.6) ½

                                = 37.75 

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.

Coefficient of variation = ( standard deviation / mean )x 100 

                                     = ( 37.75/ 18.4)x100

                                     = 20.51