Tag: interquartile range

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Questions Related to interquartile range

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

If we plot the more than type and less than type frequency distributions of the same set of date, their graph intersect at a point which is known as ______.

  1. median

  2. mode

  3. mean

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The intersection of the 'less than' ogive and the 'more than' ogive on a graph provides the median of the frequency distribution.

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

Which of the following relations among the location parameters does not hold?

  1. $Q _2 = Median$
  2. $P _50 = Median$
  3. $D _5 = Median$
  4. $D _4 = Median$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Median is the middle value, which corresponds to the 50th percentile (P50), the 5th decile (D5), and the 2nd quartile (Q2). D4 represents the 40th percentile, not the median.

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

In a group, $2$ students spend Rs$8$ daily, $3$ students spend Rs$10$ daily and $5$ students spend Rs$6$ daily. The average spending of all $10$ students is _______.

  1. $7.6$
  2. $5.8$
  3. $8.5$
  4. $6.7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total spending = (2 * 8) + (3 * 10) + (5 * 6) = 16 + 30 + 30 = 76. Total students = 10. Average = 76 / 10 = 7.6.

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

The $P _82$ for the following distribution is

X 2 3 4 5 6 7 8 9 10 11
Y 3 6 9 18 20 14 10 10 7 2


  1. $6$
  2. $5$
  3. $8$
  4. $9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total frequency N = 99. The 82nd percentile position is 0.82 * (99 + 1) = 82nd value. Looking at the cumulative frequencies (3, 9, 18, 36, 56, 70, 80, 90, 97, 99), the 82nd value falls within the category X = 9.

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

Which of the following measures of dispersion can attain a negative value?

  1. Range

  2. Mean deviation

  3. Standard deviation

  4. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Measure of dispersion is a statistical method to find a specific value from a dispersed series where the extent to which various values of the series tend to disperse from each other or from the average is measured. So all the measures of dispersion from range to standard deviation has positive value. 

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

Which measure of dispersion is most affected by extreme values?

  1. Standard deviation

  2. Mean deviation

  3. Range

  4. Quartile deviation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Range is the most simple and commonly understandable measures of dispersion.Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

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

Semi inter-quartile deviation is given by the formula _______.

  1. $Q _3 - Q _1$
  2. $\frac{Q _3 - Q _1}{8}$
  3. $\frac{(Q _3 - Q _1)}{2}$
  4. $\frac{(Q _3 - Q _1)}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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 .


Semi inter-quartile deviation = (Q3-Q1) /2

                             = (29-17)/2

                             = 12/2

                             = 6

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

Which measure of dispersion ensures lowest degree of reliability?

  1. Range

  2. Mean deviation

  3. Quartile deviation

  4. Standard deviation
Reveal answer Fill a bubble to check yourself
A Correct answer
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 affected measures of dispersion by the extreme values of the series therefore it has the lowest degree of reliability. 

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

The co-efficient of range from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

  1. $0.6$
  2. $0.5$
  3. $0.55$

  4. None of them
Reveal answer Fill a bubble to check yourself
C Correct answer
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 = H - L 
In the given series, H= 34 and L+ 10 
Range = 34-10 = 24.
Coefficient of range is found by dividing the range with the sum of highest and lowest value of the series. 
Coefficient of range (CR) = R/ (H+L) 
                                          =24 / (34+10) 
                                          = 24/ 44 = 0.55 

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

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

  1. $0.26$
  2. $0.16$
  3. $0.06$
  4. $0.36$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 .

The coefficient of quartile deviation is found by dividing the difference between the first quartile and the third quartile by the sum between the first quartile and the third quartile.

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

Q1= 17 and Q3=29 

Coefficient of quartile deviation =(Q3-Q1)/ (Q3+Q1)

                                            = (29-17)/ (29+17)

                                            = 12/46 = 0.26