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

The first quartile divides a frequency distribution in the ratio _____.

  1. $4 : 1$
  2. $1 : 4$
  3. $3 : 1$
  4. $1 : 3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The first quartile (Q1) represents the 25th percentile, meaning 25% of the data is below it and 75% is above it. The ratio of 25:75 simplifies to 1:3.

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 frequency distribution with open ends, one cannot find out ______.

  1. mean

  2. median

  3. mode

  4. all of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The arithmetic mean requires the exact values of all observations. In open-ended distributions, the exact values of the first or last classes are unknown, making the mean impossible to calculate.

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 suitable measure of central tendency for qualitative data is ______.

  1. mode

  2. arithmetic mean

  3. geometric mean

  4. median
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Median is the most suitable measure for qualitative data (ordinal data) because it is based on the position of values rather than their magnitude, which cannot be averaged numerically.

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

Mean of a set of values is based on _______.

  1. all values
  2. $50$ percent values

  3. first and last value

  4. maximum & minimum value
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The arithmetic mean is calculated by summing all values in a dataset and dividing by the count, making it dependent on every single observation.

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

For the following data:

Weekly Income (in Rs.): 58 59 60 61 62 63 64 65 66
No. of Workers: 2 3 6 15 10 5 4 3 1


The value of $\displaystyle\frac{Q _1+Q _3}{2}$ is equal to

  1. $Q _1$
  2. $Q _2$
  3. $Q _3$

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

The cumulative frequency of the table is a given below:

Weekly income ( in Rs.) No. of workers Cumulative frequency
58 2 2
59 3 5
60 6 11
61 15 26
62 10 36
63 5 41
64 4 45
65 3 48
66 1 49
N = 49


Lower Quartile: 
We have $\displaystyle\frac{N}{4} = \displaystyle\frac{49}{4} = 12.25$
The cumulative frequency just greater than $\displaystyle\frac{N}{4}$ is $26$ and the corresponding value of the variable is $61$
$\therefore\quad Q _1 = Rs.\space 61$

Middle Quartile (median): 
We have $\displaystyle\frac{N}{2} = \displaystyle\frac{49}{2} = 24.5$
The cumulative frequency just greater than $\displaystyle\frac{N}{2}$ is $26$ and the corresponding value of the variable is $61$
$\therefore\quad Q _2 = Rs.\space 61$

Upper Quartile:
We have $\displaystyle\frac{3N}{4} = \displaystyle\frac{3\times49}{4} = 36.75$
The cumulative frequency just greater than $\displaystyle\frac{3N}{4}$ is $41$ and the corresponding value of the variable is $63$
$\therefore\quad Q _3 = Rs.\space 63$

$\therefore\quad \displaystyle\frac{Q _1+Q _3}{2} = \displaystyle\frac{61+63}{2} = 62$