Tag: measures of dispersion

Questions Related to measures of dispersion

The correct relation between variance and standard deviation (S.D) of a variable X 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. S.D = Var

  2. $S.D =[ Var(X)^{\frac{1}{2}}]$

  3. $S.D = [Var(x)]^2$

  4. None of the above

Show answer
Correct Option: B
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.

Variance is the mean of the squares of the deviations from the mean. 
Standard deviation is the square root of variance or variance is the square of standard deviation. 
S.D = {Var(X)}1/2 

or 
Var(X) = (S.D)2 

For comparison of two different series, the best measure of dispersion 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. standard deviation

  2. range

  3. mean deviation

  4. coefficient of variation

Show answer
Correct Option: D
Explanation:

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series. The coefficient of standard deviation is calculated by dividing the standard deviation of the series by its mean and then multiplying it by 100. It is regarded as the best measure of dispersion to compare two different series because it is expressed in percentage. 

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

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. 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

Show answer
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

Show answer
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.