Tag: measures of dispersion and skewness

Quizzes (4) Questions (166)

Questions Related to measures of dispersion and skewness

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

Value of each sample observation is decreased by $25$, the range of the sample observation will ____________.

  1. increase by $25$

  2. remain same
  3. decrease by $25$
  4. increase by $2$ times
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Range is the difference between the maximum and minimum values. If every value is decreased by 25, both the maximum and minimum decrease by 25, so the difference (max - min) remains unchanged.

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

  1. $24$
  2. $20$
  3. $30$
  4. $42$
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 simple and commonly understandable measures of dispersion.

Range = H - L 
In the given series, H= 34 and L+ 10 
Range = 34-10 = 24.

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

From the following detail find out coefficient of Quartile Deviation.
$3=64,Q1=50$

  1. $12.11$%
  2. $12.28$%
  3. $13.50$%
  4. $12.08$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The coefficient of quartile deviation is calculated as (Q3 - Q1) / (Q3 + Q1). Given Q3 = 64 and Q1 = 50, the calculation is (64 - 50) / (64 + 50) = 14 / 114, which is approximately 0.1228 or 12.28%.

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 $Q _3$ 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
C Correct answer
Explanation

To find Q3, calculate the cumulative frequency: 3, 9, 18, 36, 56, 70, 80, 90, 97, 99. The total N is 99, so the 3rd quartile position is 0.75 * (99 + 1) = 75th value, which corresponds to X = 8.

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 $8th$ decile of the following observations is
$29, 18, 15, 30, 42, 35, 34, 28, 45, 34$

  1. $44.6$
  2. $40.6$
  3. $34.15$
  4. $38.15$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First, sort the data: 15, 18, 28, 29, 30, 34, 34, 35, 42, 45. The 8th decile (D8) is the 0.8 * (10 + 1) = 8.8th position. Interpolating between the 8th (35) and 9th (42) values: 35 + 0.8 * (42 - 35) = 35 + 5.6 = 40.6.

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

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.