Chapter 19 : Measures of Dispersion | Short Questions [2 Marks each]
1. What is the meaning of dispersion? [2016]
Answer: A measure of dispersion measures numerically the extent by which individual observations deviate from the central value on the average.
2. Define range as a measure of dispersion. [2017]
Answer: Range of a set of observations is the difference between the maximum value and the minimum value i.e., Range = Xmax – Xmin.
3. Mention two advantages of range.
Answer: Two advantages of range are:
(a) Range is easy to understand.
(b) Range is simple to calculate.
4. Mention any two disadvantages of range as a measure of dispersion. [2018, 2019]
Answer: Two disadvantages of range are:
(a) Range becomes meaningless when at least one of the two limits of the variable is infinite.
(b) Range cannot be calculated from the frequency distributions with open-end class.
5. Mention any one advantage and one disadvantage of range as a measure of dispersion. [2015]
Answer: Advantage of Range – Range is simple to calculate.
Disadvantage of Range – Range cannot be calculated from the frequency distributions with open-end class.
6. How can range be determined for a frequency distribution grouped in classes?
Answer: For a frequency distribution grouped in classes, range can be determined by the difference between the upper class boundary of the highest class and the lower class boundary of the lowest class.
7. Find the range of weights of 5 persons given below : 50kg, 55kg, 57kg, 60kg, 65kg.
Answer: Range = Xmax – Xmin = 65 – 50 = 15kg.
8. Define standard deviation. [2015]
Answer: Standard deviation of a set of observations is the square root of the A.M of squares of deviations from A.M.
9. Mention any two advantages of standard deviation. [2017]
Answer: Two advantages of standard deviation are:
(a) S.D is based on all observations.
(b) S.D is less affected by sampling fluctuations.
10. Mention any two disadvantages of standard deviation as a measure of dispersion. [2023]
Answer: Two disadvantages of standard deviation are:
(a) S.D cannot be easily calculated.
(b) S.D is not easy to interpret.
11. Standard deviation of 15 observations is 3. If each observation is doubled what will be the standard deviation?
Answer: If each observation is doubled, S.D will be the same as before i.e. 3.
12. The standard deviation of a variable x is 10. Then what will be the standard deviation of 50 + 5x.
Answer: We know If y = a + bx, then S.D of y = |b|. S.D of x.
Here, |b| = 5 and S.D of x = 10.
Therefore, S.D of y = 5 x 10 = 50.
13. “Standard deviation of 10 observations is 2. If each observation is increased by 5 the new standard deviation will be 7.” State, with reasons, whether this statement is true or not.
Answer: This statement is not correct. As the observations are increased by same value (5), mean will also be increased by 5. So, the deviation from the mean will be the same as before. That is why new S.D will be the old S.D i.e 2.
14. The value of standard deviation depends on choice of origin but not on choice of scale- Is this statement right? If not, state the right statement.
Answer: No, this is not the right statement. The correct statement is – “S.D is independent of changes in origin but not of scale”.
15. What is the relation between standard deviation and variance of a variable?
Answer: Standard Deviation (S.D) is the positive square root of variance of a variable.
16. What is Lorenz curve?
Answer: Lorenz curve is a cumulative percentage curve in which the percentage of frequency or persons is combined with the percentage of items like income, wealth, profits, wages, etc.
17. What is line of equal distribution?
Answer: The diagonal of the box diagram representing the Lorenz curve is known as the egalitarian line or the line of equal distribution.
18. Define Gini coefficient.
Answer: Lorenz ratio (R) or Gini coefficient (G) refers to Area of concentration divided by diagonal triangle of the box diagram (value 1/2). Therefore, Lorenz ratio or Gini coefficient is twice the area of concentration.
19. What are the upper and lower limits of the value of Gini coefficient?
Answer: Lorenz ratio or Gini coefficient lies between zero and unity i.e. the upper limit is 1 and lower limit is 0.
20. While drawing a Lorenz curve what is measured in which axis of coordinates?
Answer: While drawing a Lorenz curve, Cumulative proportion of persons having income less than or equal to ‘x’ in total population which is represented by P(x) is measured on the horizontal axis. Cumulative proportion of persons having income less than or equal to ‘x’ in national income of the economy which is represented by Q(x) is measured on the vertical axis.
21. If the coordinates of a point on a Lorenz curve be (P1, Q1) what do they signify?
Answer: Here P1 signifies Cumulative proportion of persons having income less than or equal to ‘x’ in total population and Q1 signifies Cumulative proportion of persons having income less than or equal to ‘x’ in national income of the economy.
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