Q.17. Discuss the special uses of geometric mean.
Ans. Geometric mean is specially used in finding out the averae of percentage changes or ratio of chang. The averages in case of population growth, price increase, growth rate, compound interest, depreciation by diminishing method, etc. are computed through geometric mean only.
Q.18. Write the two uses o geometric mean,
Ans. The two uses of geometric mean are:
- When large weights are to be given to small items and small weight to large items.
- When averages is to be calculated in a series expressing changes in terms of ratios, percentages or compound rate.
Q.19. Write the two algebraic properties of geometric mean.
Ans. If G.M. is placed in place of each value, the product of multiplication will be equal to the product of multiplication of different values.
Q.20. Define the term harmonic mean.
Ans. Harmonic mean of a series is the reciprocal of the arithmetic average of the reciprocals of the value of its various items.
Q.21 Write the formula of harmonic mean in discrete series.
Ans. Formula for harmonic mean in discrete series.
Q.22. Write the meaning of weighted harmonic mean.
Ans. If the relative importance of different values in a series is different, then weighted harmonic mean is calculated.
Q.23. Write the relationship between A.M., G.M. and H.M.
Ans. The relationship between A.M., GM. And H.M. are as:
- If all the items in a serieees have the same value, then X = G.M. = H.M.
- If all the items in a series are not equal, then A.M. > G.M. > H.M.
It means that the value of harmonic mean will be lowest, G.M. will be greater than H.M. and the value of arithmetic mean will be greater than G.M.
- If there are two items, then
Q.24. Define the term dispersion.
Ans. Dispersion literally means scatteredness. It is the spread or scatter of values from a measure of central tendency. It is studied to have an idea of the homogeneity or heterogeneity of the frequency distribution.
Q.25. Write the four characteristics of measure of dispersion.
Ans. The four Characteristics of measure of dispersion are :
- It should be rigidly defined.
- It should be based on all observations.
- It should be readily comprehensive.
- It should be simple to understand and easy to calculate.
Q.26. Write the four importances of dispersion.
Ans. The four importances of dispersion are;
- To judge the reliability of the average.
- To know the range of value.
- To make a comparative study of the variability of two or more series.
- To control variability.
Q.27. Define the meaning of mean deviation.
Ans. Mean deviation is also known as ‘Average deviation’ Or ‘first moment of dispersion’. Mean deviation of a series is the arithmetic average of the deviations of various items from a measure of central tendency (either mean, median or mode). While taking deviations, msathematical sign of plus (+) or minus (-) are ignored.
Q.28. Discuss the two merits and demerits of mean deviation.
Ans. Merits: These are as follows:
- Based on all values.
- Better measure for comparison.
Demerits: These are as follows:
- Ignoring algebraic signs.
- Increase with the size of sampling.
Q.29. Define the meaning of standard deviation.
Ans. Standard deviation (s.d) is and ideal, scientific and most popular measure dispersion. It was first used by karl pearson in the year 1893. As a definition ‘Standard deviation is the square root of the arithmetic mean of the squares of deviations of items from their arithmetic mean.’ Standard deviation can also be defined as positive square root of variance.
Q.30. Write the four points of an ideal and scientific measure of standard deviation.
Ans. S.D. is considered as and ideal and scientific measure of dispersion and there are following reasons for it.
- S.D. is based on all items of the series.
- Deviations are always taken from arithmetic mean, which is rigidly defined measure of central tendency.
- Algebraic sign of ‘+’ and ‘-‘ are considered while taking deviations.
- S.D. is fully capable of further algebraic treatment.
Q.31. Discuss the two merits and limitations of standard deviation.
Ans. Meritss: These are as follows:
- Based on all values.
- Less influence of sampling.
Limitations: These are as follows:
- Difficulty in calculation.
- More weightage to extreme values.
Q.32. Write the meaning of skewness.
Ans. The term skewness means, ‘Lack of symmetry’, i.e. if the distribution of data is not symmetrical, it is called asymmetrical or skewed. A distribution is said to be symmetrical when the frequencies are symmetrically distributed about mean, i.e. values of the variable are equidistant from the mean.
Q.33. Write the two measures of skewness.
Ans. The two measures of skewness are:
- Absolute measure of skewness.
- Relative measure of skewness.
Define the term measure of skewness is known as coefficient of skewness which is obtained by dividing the absolute measure of skewness by any of the measures of dispersion because here we are actually measuring the extent of symmetry with respect to dispersion of the items around a central value.
Q.35. write the formula of Bowley’s coefficient of skewness.
Ans. This method is based on median and both the quarties Q1 and Q3 and thus it is also knkkown as ‘Quartile coefficient of skewness’. The formula for calculating Bowley’s coefficient of skewness is: