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

When all the observations are same, the relation between A.M., G.M and H.M is _________.

  1. A.M. = G.M. = H.M.

  2. A.M. = G.M. > H.M.

  3. A.M. > G.M. > H.M.

  4. A.M. < G.M. < H.M.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When all observations in a dataset are identical, the Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM) are all equal to that constant value.

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

A frequency distribution having two modes is said to be ________.

  1. unimodal

  2. bimodal

  3. trimodal

  4. without mode
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A frequency distribution with two modes is called bimodal. Unimodal has one mode, and trimodal has three.

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

Geometric mean of two observations can be calculated only if ________.

  1. both the observations are positive

  2. one of the two observations is zero

  3. one of them is negative

  4. both of them are zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The geometric mean involves taking the nth root of the product of n numbers. If any number is negative, the root may be imaginary; if zero, the product is zero. Thus, it is typically defined for positive observations.

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

For further algebraic treatment geometric mean is _______.

  1. suitable

  2. not suitable

  3. sometime suitable

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

The geometric mean is not suitable for further algebraic treatment (like calculating the mean of means) because it is based on products rather than sums.

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

Extreme value have no effect on _______.

  1. average

  2. median

  3. geometric mean

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

The median is a positional average and is not affected by extreme values (outliers) in the dataset, unlike the arithmetic mean.

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 modal value is not clear in a distribution, it can be ascertained by the method of ________.

  1. grouping

  2. guessing

  3. summarizing

  4. trial and error
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the mode is not clearly identifiable in a frequency distribution, the grouping method is used to determine the modal class or value.

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

For further algebraic treatment harmonic mean is ______.

  1. suitable

  2. not suitable

  3. sometime suitable

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

Like the geometric mean, the harmonic mean is not suitable for further algebraic treatment because it is based on the reciprocal of the values.

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

Harmonic mean gives more weight age to _______.

  1. small values

  2. large values

  3. positive values

  4. negative values
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Harmonic mean gives more weight to smaller values because of the reciprocal in its formula. A small number becomes large when reciprocated, dominating the calculation.

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

Mean deviation of $7,10,10,15,10,8,8,7,3,2,10$ through mean is

  1. $3.14$
  2. $8$
  3. $\dfrac {4}{5}$

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

mean $=\dfrac{\sum {x _1}}{n}=\dfrac{90}{11}\approx 8.18$

derivation through mean = $|x _i-\bar x|$
& mean of it is $=\dfrac{\sum|{x _i-\bar x}|}{n}$
$=\dfrac{(1.18+1.82+1.82+6.82+8.18+0.18+0.18+1.18+5.18+6.18+1.82)}{11}$
$=\dfrac{34.54}{11}=3.14$