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# Measures of dispersion.. Statistics& Library and information science

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### Measures of dispersion.. Statistics& Library and information science

1. 1. Harsha E.C. CUANLIS008 University of Calicut
2. 2. Dispersion Dispersion or spread is the degree of the scatter or variations of the variables about a central value  Range  Quartile deviation  Mean deviation  Standard deviation  Lorenz curve
3. 3. Properties For An Ideal Measure Of Dispersion o It should be rigidly defined o It should be easy to understand o It should be simple to calculate o It should be based on all observation of series o It should be capable of further algebraic manipulation o It should not be affected much by extreme observation
4. 4. Measures of Dispersion Algebraic method Graphic (Absolute and relative) ( Lorenz curve) Range Quartile deviation Mean deviation Standard deviation Full range Quasi range Quartile range Percentile range Coefficient of the respective range
5. 5. Range o Range is the difference between the largest value (L) and the Smallest value(S) in a distribution ( R= L-S) o Higher value of range implies higher dispersion and vice versa o It can be calculated even when few observation are missing . It is not based on all the values. As long as the minimum and maximum values are remain unaltered, any changes in other values does not affect range o Coefficient of range:- Derived by dividing a given range by the sum of the two boundary values taken in to account for calculating range. On the other hand the relative measure corresponding to range , called coefficient of range.
6. 6. Merits and Demerits o It is simple to understand o It is easy to compute o It is very rough measure of dispersion o If there are one or two abnormal items, range will give very misleading result o It can’t be computed from frequency distributions with open end classes o Range do not take in to account of entire distribution
7. 7. Quartile Deviation o Quartile Deviation is a measure of dispersion based on the third quartile (Q3) and the first quartile(Q1) o The difference between the values of two quartile (Q3-Q1)is what is called Inter Quartile Deviation o Q. D =Q3-Q1/2 Coefficient of Q.D= Q3-Q1/Q3+Q1 o It is also known as 50% zone o It is a measure of location as well as a measure of dispersion
8. 8. (1) Q1 (3) (2) Q3 (3) (4) A 50% B
9. 9. o It is easy to understand and calculate o It is better measure than range o It is not effected by extreme values o It can be found graphically o Q.D is affected considerably by fluctuations of sampling o Q.D is not suitable for further mathematical treatment Merits& Demerits
10. 10. Mean Deviation Clark and schkade has defined ‘’ Average Deviation is the average amount of scatter of that items in a distribution from either the mean or the median , ignoring the sign of the deviation. The average that is taken of the scatter is an arithmetic mean which account for the fact that this measure is often called the mean deviation’’ Mean deviation is a measure in the determination of which the items are taken in to account. The calculation of mean deviation is comparatively difficult than that of the quartile deviation
11. 11. Merits& Demerits o Mean deviation is rigidly defined o It is simple to calculate and can easily be understood o It is based on all the observations of a series o It is less affected by extreme items as compared with S.D. o It is not suitable for large sample or grounded data o It is not accurate measure of dispersion specifically where it is computed from mode o It can’t be completed for distributions with open and classes
12. 12. Standard deviation o Introduced by Karl Pearson in 1983 o Square root of the arithmetic mean of the square of deviation from the arithmetic mean o Denoted by the Greek letter Sigma o It is very rigidly defined o It’s computation is based on all the observation o It is the most widely useful measure of dispersion o Calculated from arithmetic mean
13. 13. Merits & Demerits o It’s value is based on all observations of a series o It is rigidly defined o It is capable of further algebraic manipulation o It is less affected by the fluctuation of sampling o It is also useful in biological statistics o It is affected by extreme value like mean deviation o Standard deviation is neither easy to understand nor so simple to calculate
14. 14. Lorenz Curve o It is the graphical measure . It uses the information expressed in a cumulative manner to indicate the degree of variability o It is specifically useful in comparing the variability of two or more distributions
15. 15. Conclusion o Measures of Dispersion  Range  Quartile deviation  Mean deviation  Standard deviation  Lorenz curve