Tag: measures of dispersion and skewness

Questions Related to measures of dispersion and skewness

If the minimum value in a set is $15$ and its range is $55$, the maximum value of the set is _______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $40$

  2. $60$

  3. $80$

  4. $70$

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Correct Option: D
Explanation:

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.

Range = 55

In the given series, H= x and L= 15

Range => x-15 = 55

            => x = 55+15 = 70 

When a line connects points that are the cumulative percent of observation below the upper limit of each interval in a cumulative frequency distribution is known as ______________.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. Mode

  2. Histogram

  3. Frequency polygon

  4. Ogive

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Correct Option: D

Range of a set of values is $60$ and maximum value in the series is $80$. The minimum value of the series is _______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $140$

  2. $20$

  3. $70$

  4. None of the above

Show answer
Correct Option: B
Explanation:

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. 

Range = 60 

In the given series, H= 80 and L= x 

Range => 80-x = 60

            => x = 80-60 = 20 

If $Q 3 + Q _1 = 108, Q _3 - Q _1 = 74$; then Q.D is ______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $33$

  2. $3.7$

  3. $37$

  4. $0.68$

Show answer
Correct Option: C
Explanation:

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 .


Quartile deviation = (Q3-Q1) /2

                             = 74/2

                             = 37

Quartile deviation is equal to _______.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. semi - interquartile range

  2. double the interquartile range

  3. interquartile range

  4. none of the above

Show answer
Correct Option: A
Explanation:

 

Quartile deviation also known as semi inter-quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 .

Quartile deviation or semi inter-quartile deviation = (Q3-Q1) /2


Whenever we group data into classes it is recommended that we have _________.

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. Less than 5 classes

  2. Between 5 and 20 classes

  3. At least 2 classes

  4. Between 2 and 3 classes

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Correct Option: B

Which measure of dispersion can be calculated in case of open end intervals?

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. Range

  2. Standard deviation

  3. Quartile deviation

  4. Coefficient of variation

Show answer
Correct Option: C
Explanation:

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 . Since quartile deviation is not affected by the extreme values of the series. Therefore, it can be calculated in case of open end intervals also. 

If the mean and standard deviation of a normal distribution are $33$ and $5$ respectively, what is the Inter-quartile range?

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. $(6.67)$

  2. $(8)$

  3. $(7.74)$

  4. $(6.8)$

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Correct Option: A

Which one of the following is a false description?

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. In a moderately asymmetrical distribution, the empirical relationship between Mean, Mode and Median suggested by Karl Pearson is Mean Mode = 3 (Mean Median)

  2. Coeffcient of variation is an absolute measure of dispersion

  3. Measure of skewness in the distribution of numerical values in the data set

  4. Kurtosis refers to the degree of flatness or peakedness in the region around the mode of a frequency curve

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Correct Option: B

The following data show the number of hours worked by 200 statistics students:

Number of Hours Frequency
0-9 40
10-19 50
20-29 70
30-39 40

The class width for this distribution is.........

business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

  1. 9

  2. 10

  3. 11

  4. Varies from class to class

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Correct Option: B