Tag: histograms and frequency distribution diagrams

Quizzes (4) Questions (65)

Questions Related to histograms and frequency distribution diagrams

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 variance of $1, 2, 4, 5$ and x is $2$, then x is _____.

  1. $3$
  2. $6$
  3. $1$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Variance = sum((x_i - mean)^2) / n = 2. For data 1, 2, 4, 5, x, the mean is (12 + x) / 5. Solving for x where variance is 2 leads to x = 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

Which measure of dispersion is least affected by extreme values?

  1. Range

  2. Mean deviation

  3. Standard deviation

  4. Quartile deviation
Reveal answer Fill a bubble to check yourself
D 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 . Therefore, quartile deviation is not affected by the extreme values of the series. 

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

Sum of squares of the deviations is minimum when deviations are taken from ________.

  1. mean

  2. median

  3. mode

  4. zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Mean deviation is the arithmetic average of the deviations of the observed values from an  average of the observed values. 
Mean deviation from the mean calculates the arithmetic average of the deviations of the observed values from mean of the observed values. Sum of the squares of the deviations is minimum when deviations are taken from mean as mean is the arithmetic average of the series and disperse the whole series into individual minimum value therefore the sum of their squares is minimum. 
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 quartile deviation from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

  1. $8$
  2. $6$
  3. $10$
  4. $5$
Reveal answer Fill a bubble to check yourself
B 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 .

In the given series, 10, 15,17,18,20,22,25,28,29,32,34 

Q1= 17 and Q3=29

Therefore, Quartile deviation = (Q3-Q1) /2

                                                 = (29-17)/2

                                                  = 12/2

                                                  = 6

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

Given the following set of data, what is the range 12 23 34 54 21 8 9 67:

  1. 55

  2. 59

  3. 8

  4. 56
Reveal answer Fill a bubble to check yourself
A 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. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

Range = H - L 

In the given series, H= 67 and L= 12 

Range = 67 -12 = 55 .

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