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 shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

What will be the relative range, if the spread of items in a given distribution lies between $100$ and $180$kg?

  1. $0.5$
  2. $0.4$
  3. $0.3$
  4. $0.55$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative range is calculated as (Max - Min) / (Max + Min). Here, (180 - 100) / (180 + 100) = 80 / 280 = 8 / 28 = 2 / 7, which is approximately 0.2857, rounding to 0.3.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

An index is at 100 in 1991. It rises 5% in 1992, falls 6% in 1993,falls 5% in 1994, rises 4% in 1995 and 7% in 1996.The index numbers for all these years with 1991 as base are _______.

  1. 100, 105, 94, 105, 95, 107

  2. 100, 105, 94, 105, 107, 95

  3. 100, 105, 94, 107, 95, 94

  4. 100, 105, 94, 95, 104, 107
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The standard deviation of $5$ items is found to be $15$. What will be the standard deviation if the values of all the items are increased by $5$?

  1. $15$
  2. $20$
  3. $10$

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

Standard deviation is independent of the change of origin. Adding a constant to all items does not change the spread of the data.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The mean of $100$ observations is $18.4$ and sum of sqares of deviations from mean is $1444$, the Co-efficient of variation is ______.

  1. $30.6$
  2. $35.6$
  3. $20.6$
  4. $10.6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standard deviation = sqrt(Sum of squared deviations / N) = sqrt(1444 / 100) = sqrt(14.44) = 3.8. Coefficient of Variation (CV) = (SD / Mean) * 100 = (3.8 / 18.4) * 100 = 20.65.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The first quartile of the following observations is
$10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23$.

  1. $17.55$
  2. $18$
  3. $15$
  4. $20$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sorted data: 10, 14, 15, 16, 18, 18, 18, 19, 20, 22, 23. N=11. First quartile (Q1) position = (N+1)/4 = 12/4 = 3rd value. The 3rd value is 15.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The following distribution of ages (in complete years) is obtained for the students of higher secondary.
The mode of the distribution is.

Age (in years) 15 16 17 18 19 20 21
Number of students 12 18 20 10 7 6 2





  1. $16$
  2. $17$
  3. $18$

  4. None of them
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mode is the value with the highest frequency. Here, age 17 has the highest frequency of 20 students.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The median 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
A Correct answer
Explanation

Total frequency = 3+6+9+18+20+14+10+10+7+2 = 99. Median is the (99+1)/2 = 50th value. Cumulative frequencies: 3, 9, 18, 36, 56. The 50th value falls in the category where X=6.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The mean of $25$ observations is $73.408$. If one observation $64$ is removed, the revised mean is ______.

  1. $72.8$
  2. $73.8$
  3. $80.8$
  4. $76.8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original sum = 25 * 73.408 = 1835.2. New sum = 1835.2 - 64 = 1771.2. New mean = 1771.2 / 24 = 73.8.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The correct relation between variance and standard deviation (S.D) of a variable X is _______.

  1. S.D = Var
  2. $S.D =[ Var(X)^{\frac{1}{2}}]$
  3. $S.D = [Var(x)]^2$

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

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Variance is the mean of the squares of the deviations from the mean. 
Standard deviation is the square root of variance or variance is the square of standard deviation. 
S.D = {Var(X)}1/2 

or 
Var(X) = (S.D)2 

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

For comparison of two different series, the best measure of dispersion is _________.

  1. standard deviation

  2. range

  3. mean deviation

  4. coefficient of variation
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series. The coefficient of standard deviation is calculated by dividing the standard deviation of the series by its mean and then multiplying it by 100. It is regarded as the best measure of dispersion to compare two different series because it is expressed in percentage.