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

If the minimum value in a set is $15$ and its range is $55$, the maximum value of the set is _______.

  1. $40$
  2. $60$
  3. $80$
  4. $70$
Reveal answer Fill a bubble to check yourself
D 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 = 55

In the given series, H= x and L= 15

Range => x-15 = 55

            => x = 55+15 = 70 

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

When a line connects points that are the cumulative percent of observation below the upper limit of each interval in a cumulative frequency distribution is known as ______________.

  1. Mode

  2. Histogram

  3. Frequency polygon

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

An ogive is a graphical representation of a cumulative frequency distribution, where points are plotted at the upper limits of intervals.

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

Range of a set of values is $60$ and maximum value in the series is $80$. The minimum value of the series is _______.

  1. $140$
  2. $20$
  3. $70$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B 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 = 60 

In the given series, H= 80 and L= x 

Range => 80-x = 60

            => x = 80-60 = 20 

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 $Q 3 + Q _1 = 108, Q _3 - Q _1 = 74$; then Q.D is ______.

  1. $33$
  2. $3.7$
  3. $37$
  4. $0.68$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 .


Quartile deviation = (Q3-Q1) /2

                             = 74/2

                             = 37

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

Quartile deviation is equal to _______.

  1. semi - interquartile range

  2. double the interquartile range

  3. interquartile range

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

 

Quartile deviation also known as semi inter-quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 .

Quartile deviation or semi inter-quartile deviation = (Q3-Q1) /2


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

Whenever we group data into classes it is recommended that we have _________.

  1. Less than 5 classes

  2. Between 5 and 20 classes

  3. At least 2 classes

  4. Between 2 and 3 classes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sturges' rule and general statistical practice suggest that for most data sets, having between 5 and 20 classes provides a good balance between detail and clarity.

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 measure of dispersion can be calculated in case of open end intervals?

  1. Range

  2. Standard deviation

  3. Quartile deviation

  4. Coefficient of variation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 . Since quartile deviation is not affected by the extreme values of the series. Therefore, it can be calculated in case of open end intervals also. 

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 the mean and standard deviation of a normal distribution are $33$ and $5$ respectively, what is the Inter-quartile range?

  1. $(6.67)$
  2. $(8)$
  3. $(7.74)$
  4. $(6.8)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, the inter-quartile range (IQR) is approximately 1.3489 times the standard deviation. 1.3489 * 5 = 6.7445, which is closest to 6.67.

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 one of the following is a false description?

  1. In a moderately asymmetrical distribution, the empirical relationship between Mean, Mode and Median suggested by Karl Pearson is Mean Mode = 3 (Mean Median)

  2. Coeffcient of variation is an absolute measure of dispersion

  3. Measure of skewness in the distribution of numerical values in the data set

  4. Kurtosis refers to the degree of flatness or peakedness in the region around the mode of a frequency curve
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The coefficient of variation is a relative measure of dispersion, not an absolute one, because it is expressed as a percentage or ratio of the mean.

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 following data show the number of hours worked by 200 statistics students:

Number of Hours Frequency
0-9 40
10-19 50
20-29 70
30-39 40

The class width for this distribution is.........

  1. 9

  2. 10

  3. 11

  4. Varies from class to class
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Class width is the difference between the upper boundary of a class and the lower boundary. For 0-9, 10-19, the width is 10 - 0 = 10.