Meaning of Variability and its measures .pptx

Meaning of Variability and its measures

1. Variability :- Dr. Makarand Joshi Associate professor MSM’s COPE

2. Variability :- Meaning and definition of variability :- A cursory look at the graphical representation of 3 figures of normal curve enable us to know that the two random samples may have a common mean but still may differ in the scatter of their individual values.

3. The two groups may have widely different mean value but may have a comparable spread of variability of its individual scores and most frequently, the two groups have their individual mean value and scatters. The spread of a group's individual scores from lowest value to highest value or despersions from the mean value is known as the variability of the group under study.

4. Types of Variability Test :- The central aim of all the test measures of variability is to record deviation of individual values below and above the mean value or to define the limits of the entire scatter of values .  Generally the variability is measured with the help of following test.

5. 1) Range. 2) Average Deviation. 3) Quartile Deviation. 4) Standard Deviation. 5 ) Variance. 6) Coefficient of Variance

6. A) Range :- Range is the easiest test of variability and is commonly referred term in variety of statistical situations. Range is a distance and unlike mean. It is not a single location the range is defined as, "The distance from the lowest value to the highest value among a series of scores".

7. Range is calculated by the following mathematical equation :-   R =  ( H - L ) + 1. B) Average Deviation :- It is the average of all the individual deviations from the mean value of the group irrespective of the +/- sign of deviation.

8. Mathematically formula of AD.                              _                    £( X - X )       AD =. ---------------------                          N £ = Sum of. N = Number of individual values. X = Individual value. X = Mean value.

9. The average deviation is somewhat better indicator of measurement of variability as it gives an average distance of scatter of the sample with respect to its mean value. Whereas range does not give any reference to the central tendency or  mean. It is a rough approximation of standard deviation, (the calculation of which involves somewhat Complex time-consuming steps), but with the the invention and easy access of calculators the use of Average Deviation is on the decrease and is being replaced by Standard Deviation.

10. C) Quartile deviation (QD) This measure of variability indicates one half of the distance between the first and third quartile points of a distribution which compares middle 50% of the total number of individual values from the mean for mediam value. It is calculated by the following formula :-                        Q3 - Q1 A)        QD = --------------                               2

11.                         P   75 - P 25   B)       QD = ------------------                                 2 Q3 = 3rd quartile for 75th percentile. Q1 = 1st quartile for 25th percentile. The quartile deviation is also known as semi interquartile range. It is used when the distribution is skewed and contains a few extreme scores or when the distribution is irregular.

12. D) Standard Deviation (SD ) : - It is regarded as the most reliable and stable testing of variability and is most widely used. It is indispensable when further statistical computation (say ,  in the form of correlation Coefficient for significance of difference between means etc.) is also to be calculated.

13. The standard division is defined as ,  "Square root of the average of the squares of the individual deviation scores from the mean value".Or "Square root of the mean of the squares of the deviations of scores from their mean value". Standard Deviation is also defined as, "the square root of variance". Method of computing SD :-

14.                             (£X)2                  £x2 - --------------                                   N                  -------------------------------                                 N - 1 SD = ( Inroot ) X = Individual score. x = Mean of the given set of score. N = Total number of score.

15. E) Variance :- It is also a reliable and useful measures of variability and may be defined as, "the mean of the squares of the deviations of scores from their mean". In other words, it is equal to the square of standard deviation rather it is the last but one step in the calculation of standard deviation and is used in inferential statistics.

16. F) Coefficient of of Variation :- This measure of variability is used to compare the variation of two or more variables having different units of measurement because it eliminates the units by converting standard deviation into a coefficient. It may be defined as, "the standard deviation in percentage of the mean value".

17. It is computed by the following equation – Coefficient of Variation (CV)                    SD        =    ----------------- × 100                   Mean