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 for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

If a constant value $40$ is subtracted from each observation of a set, the mean of the set is __________.

  1. increased by $40$
  2. decreased by $40$

  3. is not affected

  4. zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If a constant is subtracted from every observation in a set, the mean of the set is also decreased by that same constant.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

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

  1. $17.55$
  2. $18$
  3. $15$
  4. $16.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mode is the value that appears most frequently. In the set 10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23, the number 18 appears three times, which is more than any other number.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

The second 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
B Correct answer
Explanation

The second quartile (Q2) is the median. First, sort the data: 10, 14, 15, 16, 18, 18, 18, 19, 20, 22, 23. With 11 observations, the median is the 6th value, which is 18.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

If Md, Q, D and P Stands for median, quartile, decile and percentile respectively, then which of the following relation between them is true?

  1. $M _d = Q _2 = D _6 = P _50$
  2. $M _d = Q _3 = D _6 = P _75$
  3. $M _d = Q _5 = D _5 = P _50$
  4. $M _d = Q _2 = D _5 = P _50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The median (Md) divides the data into two halves (50%), the second quartile (Q2) is the median, the 5th decile (D5) is the median, and the 50th percentile (P50) is the median. Thus, Md = Q2 = D5 = P50.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

Which of the following relation is true between $3^{rd}$ decile and $30^{th}$ percentile?

  1. $D _7 = P _{70}$
  2. $D _7 = P _{30}$
  3. $D _3 = P _{30}$
  4. $D _3 = P _{70}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Deciles divide data into 10 parts, so D3 represents 30% of the data. Percentiles divide data into 100 parts, so P30 also represents 30% of the data. Therefore, D3 = P30.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

The A.M of two numbers is $6.5$ and their G.M is $6$. The two numbers are _____.

  1. $8, 6$
  2. $8, 5$
  3. $7, 16$
  4. $4, 9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given AM = (a+b)/2 = 6.5, so a+b = 13. Given GM = sqrt(ab) = 6, so ab = 36. The numbers 4 and 9 satisfy a+b = 13 and ab = 36.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

Mode is that value in a frequency distribution which possesses __________.

  1. minimum frequency

  2. maximum frequency

  3. frequency one

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

By definition, the mode of a frequency distribution is the value that occurs most frequently, meaning it has the maximum frequency.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

In a discrete series having $(2n+1)$ observations, median is ______.

  1. nth observation
  2. $(n+1)$th observation
  3. $[(n+2)/2]th$ observation
  4. $[(2n+1)/2]th$ observation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a series with N observations, if N is odd, the median is the ((N+1)/2)th observation. Substituting N = 2n+1 gives ((2n+1+1)/2)th = (2n+2)/2 = (n+1)th observation.