Q.1. Define dispersion.
Ans. Dispersion is the extent to which values in a distribution vary from the average of the distribution.
Q.2. Name the two types of measures.
Ans. Measures of dispersion can be classified as absolute measures and relative measures.
Q.3. Define absolute measures of dispersion.
Ans. Absolute measures of dispersion are expressed in terms of original units of a data.
Q.4. List the methods of absolute measures of dispersion.
Ans. The methods of absolute measures of dispersion are:
(i) Range
(ii) Quartile deviation
(iii) Mean deviation
(iv) Standard deviation
Q.5. What are relative measures of dispersion?
Ans. Relative measures of dispersion are expressed in terms of percentage and ratios. Coefficient of range, coefficient of quartile deviation, coefficient of mean deviation and coefficient of variance are the relative measures of dispersion.
Q.6. Why is it important to know the spread of values?
Ans. The averages tell only one aspect of a distribution, that is, a representative size of the values. It important to know the spread of values to understand averages in a better manner.
Q.7. Discuss the features of a good measure of dispersion?
Ans. The following are the features of a good measure of dispersion:
(i) It should be simple to understand and easy to calculate.
(ii) It should be rigidly defined.
(iii) It should be based upon all values of the given distribution.
(iv) It should be capable of advanced mathematical treatment.
(v) It should have sampling stability.
(vi) It should be not be unduly affected by extreme values.
Q.8. Distinguish between absolute and relative measures of dispersion.
Ans. Following are the points of difference between absolute and relative measures of dispersion:
1. Absolute Measures of Dispersion
Absolute measures of dispersion are expressed in terms of original units of a data. The methods of absolute measures of dispersion are:
2. Relative Measures of Dispersion
Relative measures of dispersion are expressed in terms of percentage and ratios. The methods of relative measures of dispersion are coefficient of:
Q.9. State the limitations of absolute measures of dispersion.
Ans. Following are the limitations of absolute measures of dispersion:
(i) Absolute measures may give misleading ideas about the degree of variation.
(ii) They give answer in the units in which original values are expressed thereby making them inappropriate for comparison.
Q.10. What are the objectives of measuring dispersion?
Ans. The objectives of measuring dispersion are:
(i) To determine the reliability of the average
(ii) To compare the variability of two or more distributions
(iii) To facilitate the use of other statistical methods
(iv) To know the nature and hence, control the reasons of variation
Q.11. Define range.
Ans. Range is the difference between the highest value and the lowest value in a series.
Q.12. Give the formula for finding range.
Ans. The formula for finding range (R) is:
R = H – L
where; H = Highest value in a series
L = Lowest value in a series
Q.13. What is the coefficient of range?
Ans. Coefficient of range is the ratio of the difference between the highest and lowest values of the series to the sum of the lowest and highest values of the series.
Q.14. State the merits of range.
Ans. Following are the merits of range:
(i) It is easy to understand and calculate.
(ii) It is widely used.
(iii) Its calculation takes lesser time.
Q.15. What are the limitations of range?
Ans. Following are the limitations of range:
(i) Range is unduly affected by extreme values.
(ii) It does not include all the values of the distribution.
(iii) It is not affected by the variation in the midvalues of the series.
(iv) It cannot be calculated for openended frequency distribution.
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