Tag: measures of dispersion

Questions Related to measures of dispersion

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

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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. $10.6$

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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.

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 


If A and B are two events which have no point in common, the events A and B are ______.

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. complementary to each other

  2. independent

  3. mutually exclusive

  4. dependent

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Correct Option: C
Explanation:

In probability two events are said to be independent if the occurrence of one event is not affected by the occurrence of another event. Both the variable are completely independent of each other. These events are also known as mutually exclusive event as they have no common point. 

Which of the following statements is true of a measure of dispersion?

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 does not follow algebraic value

  2. Range is crudest measure

  3. Coefficient of variation is a relative measure

  4. All the above statements

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Correct Option: D
Explanation:

  • Mean deviation is the arithmetic average of the deviations of the observed values from an  average of the observed values. Since Mean deviation do not include negative value of the deviations. Therefore, it does not follow the algebraic value of the deviations.
  • Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Since it is the most affected measures of dispersion by the extreme values of the series, it is regarded as the crudest measure. 
  • Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion. 

The relation between variance and 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. variance is the square root of standard Deviation

  2. square of the standard deviation is equal to Variance

  3. variance is equal to standard deviation

  4. standard deviation is the square of the variance

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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

Frequency 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. Tabular arrangement of data with corresponding frequency

  2. Graphical arrangement of data with corresponding frequency

  3. Tabular arrangement of data without corresponding frequency

  4. Graphical arrangement of data without corresponding frequency

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Correct Option: A

Probability can take values from ______.

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. -3 to 3

  2. -3 to 1

  3. 0 to 1

  4. -1 to 1

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Correct Option: C
Explanation:
Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1. 

A student obtained the mean and the standard deviation of 100 observations as 40 and 5.1. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and the S. D.

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 = 38.8, S. D. = 5

  2. Mean = 39.9, S. D. = 5

  3. Mean = 39.9, S. D. = 4

  4. None

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Correct Option: A

If the coefficient of correlation between $x,y$ is $0.7$ and covariance is $35$ find the standard deviation of $y$ if the standard deviation of $x$ is $5$____.

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. $10$

  2. $9$

  3. $8$

  4. $11$

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Correct Option: A

The standard deviation of sample of 30 observations is 1532. If the value of each item of the observation is increased by 5. The new standard deviation 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. same as original

  2. increased by 5

  3. reduced by 5

  4. reduced by 5 times.

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Correct Option: A