Tag: measures of dispersion and skewness

Questions Related to measures of dispersion and skewness

The first quartile divides a frequency distribution in the ratio _____.

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

  1. $4 : 1$

  2. $1 : 4$

  3. $3 : 1$

  4. $1 : 3$

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Correct Option: D

In a frequency distribution with open ends, one cannot find out ______.

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. all of the above

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Correct Option: A

if $25%$ of the items are less then $10% and 25%$are more than $40$ then the coefficient of quartile deviation 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. $30$

  2. $50$

  3. $1.2$

  4. $0.6$

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Correct Option: A

The suitable measure of central tendency for qualitative data 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. mode

  2. arithmetic mean

  3. geometric mean

  4. median

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Correct Option: D

The first quartile is also 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. median

  2. lower quartile

  3. mode

  4. third decile

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Correct Option: B

The third quartile is also called ________.

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

  1. lower quartile

  2. median

  3. mode

  4. upper quartile

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Correct Option: D

The number of partition values in case of quartiles 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. $4$

  2. $3$

  3. $2$

  4. $1$

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Correct Option: B

From which average sum of deviations is zero?

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

  1. Median

  2. Mean

  3. Mode

  4. None of them

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Correct Option: B

Mean of a set of values is based on _______.

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

  1. all values

  2. $50$ percent values

  3. first and last value

  4. maximum & minimum value

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Correct Option: A

For the following data:

Weekly Income (in Rs.): 58 59 60 61 62 63 64 65 66
No. of Workers: 2 3 6 15 10 5 4 3 1


The value of $\displaystyle\frac{Q _1+Q _3}{2}$ 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. $Q _1$

  2. $Q _2$

  3. $Q _3$

  4. None of these

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Correct Option: D
Explanation:

The cumulative frequency of the table is a given below:

Weekly income ( in Rs.) No. of workers Cumulative frequency
58 2 2
59 3 5
60 6 11
61 15 26
62 10 36
63 5 41
64 4 45
65 3 48
66 1 49
N = 49


Lower Quartile: 
We have $\displaystyle\frac{N}{4} = \displaystyle\frac{49}{4} = 12.25$
The cumulative frequency just greater than $\displaystyle\frac{N}{4}$ is $26$ and the corresponding value of the variable is $61$
$\therefore\quad Q _1 = Rs.\space 61$

Middle Quartile (median): 
We have $\displaystyle\frac{N}{2} = \displaystyle\frac{49}{2} = 24.5$
The cumulative frequency just greater than $\displaystyle\frac{N}{2}$ is $26$ and the corresponding value of the variable is $61$
$\therefore\quad Q _2 = Rs.\space 61$

Upper Quartile:
We have $\displaystyle\frac{3N}{4} = \displaystyle\frac{3\times49}{4} = 36.75$
The cumulative frequency just greater than $\displaystyle\frac{3N}{4}$ is $41$ and the corresponding value of the variable is $63$
$\therefore\quad Q _3 = Rs.\space 63$

$\therefore\quad \displaystyle\frac{Q _1+Q _3}{2} = \displaystyle\frac{61+63}{2} = 62$