Tag: histograms and frequency distribution diagrams

Questions Related to histograms and frequency distribution diagrams

The variance of $1, 2, 4, 5$ and x is $2$, then x 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. $3$

  2. $6$

  3. $1$

  4. $2$

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Correct Option: A

Which measure of dispersion is least affected by extreme values?

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. Mean deviation

  3. Standard deviation

  4. Quartile deviation

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Correct Option: D
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 . Therefore, quartile deviation is not affected by the extreme values of the series. 

Sum of squares of the deviations is minimum when deviations are taken from ________.

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

  1. mean

  2. median

  3. mode

  4. zero

Show answer
Correct Option: A
Explanation:
Mean deviation is the arithmetic average of the deviations of the observed values from an  average of the observed values. 
Mean deviation from the mean calculates the arithmetic average of the deviations of the observed values from mean of the observed values. Sum of the squares of the deviations is minimum when deviations are taken from mean as mean is the arithmetic average of the series and disperse the whole series into individual minimum value therefore the sum of their squares is minimum. 

The quartile deviation from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

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

  1. $8$

  2. $6$

  3. $10$

  4. $5$

Show answer
Correct Option: B
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 .

In the given series, 10, 15,17,18,20,22,25,28,29,32,34 

Q1= 17 and Q3=29

Therefore, Quartile deviation = (Q3-Q1) /2

                                                 = (29-17)/2

                                                  = 12/2

                                                  = 6

Given the following set of data, what is the range 12 23 34 54 21 8 9 67:

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

  1. 55

  2. 59

  3. 8

  4. 56

Show answer
Correct Option: A
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. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

Range = H - L 

In the given series, H= 67 and L= 12 

Range = 67 -12 = 55 .

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. $70$

Show answer
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