Variety of characteristic. Criteria, which determine the level of variety.

1. Variety of characteristic. Criteria, which determine the level of variety.

2. Introduction to Types of variables in statistics: A quantity, which can assume a range of numerical values, is known as a variable in statistics. For example, suppose we let the variable x representing the number of defective units in the bulbs produced. Since x is a number, the variable x could take on any value from 0.

4. RELATIVE VALUES Some Types of Variables in Statistics Quantitative variables Qualitative variables

6. Types of Variables

7. Example Researchers wish to know if the data they have collected provide sufficient evidence to indicate a difference in mean serum uric acid levels between individuals with Down’s syndrome and 15 normal individuals. The means are X1=4.5 mg/100ml and X2 =3.4 mg/100 ml.

11. The test based on the assumptions • The data of two samples follow normal distribution • The variance of the two samples are of no difference (equal).

12. F test for comparison two variances--F test • F= (bigger) (smaller) V1=n1-1 V2=n2-1 Compare F to the critical value in F distribution, get p value.

13. Destructive index Of lung • Nonsmokers: 18.1, 6.0, 10.8, 11.0, 7.7, 17.9, 8.5, 13.0, 18.9 (n1=9) • Smokers: 16.6, 13.9, 11.3, 26.5, 17.4, 15.3, 15.8, 12.3, 18.6, 12.0, 24.1, 16.5, 21.8, 16.3, 23.4, 18.8 (n2=16) • Source: D.H. Eidelman, H.Ghezzo, W.D. Kim, and M.G.Cosio, “ the destructive index and early lung destruction in smokers,” American Review of Respiratory Disease, 144,(1991), 156-159

14. Database for software-based analysis destructive index Of lung group smokers nonsmokers

16. Qualitative Variables Qualitative variable is the first type of variable in statistics. They are variables which cannot be measured.  They are also known as attributes.  It is divided into two. • a) Nominal variable • b) Ordinal variables • c) Interval variable • d) Ratio variables

19. Nominal variables Nominal data are categories that have no numerical meaning such as one's religious denomination or city or residence. The values can't logically be added, subtracted, or even sorted.

21. Quantitative variables Discrete variable Quantitative variable is the second type of variable in statistics Continuous variable

24. Continuous variables Continuous variables are those variables, which can take all the values from a given range. i.e  it can take any value between the highest and lowest value in the series. Example 1) Height of a person.  Here height can assume any value.  If the height of a person is between 142 and 152, the answer can be any value between 142 and 152 So “height of a person “ is a continuous variable.

26. Ordinal variables Ordinal data are categories also, but they can be sorted in some logical fashion such as class (junior, senior).

27. Discrete variables Discrete variables are those variables, which can take only selected values from a given range. So there will be only a finite number of values in the given range. Example 1) Number of children in a family.  Here we will get values 0,1,2…for the variables.  If the number of children is between 3 and 5, the answer will be only 4.  That is between 3 and 5, the variable can take only a selected value 4. So “number of children in a family is a discrete variable.

28. Criteria, which determine the level of variety • Limit is it is the meaning of edge variant in a variation row lim = Vmin Vmax

29. Criteria, which determine the level of variety • Amplitude is the difference of edge variant of variation row Am = Vmax - Vmin

30. Criteria, which determine the level of variety • Average quadratic deviation characterizes dispersion of the variants around an ordinary value (inside structure of totalities).

31. Average quadratic deviation σ = simple arithmetical method

32. Average quadratic deviation d = V - M genuine declination of variants from the true middle arithmetic

33. Average quadratic deviation σ = i method of moments

34. Average quadratic deviation is needed for: 1. Estimations of typicalness of the middle arithmetic (М is typical for this row, if σ is less than 1/3 of average) value. 2. Getting the error of average value. 3. Determination of average norm of the phenomenon, which is studied (М±1σ), sub norm (М±2σ) and edge deviations (М±3σ). 4. For construction of sigmal net at the estimation of physical development of an individual.

35. Average quadratic deviation This dispersion a variant around of average characterizes an average quadratic deviation (  )

36. Criteria, which determine the level of variety • Coefficient of variation is the relative measure of variety; it is a percent correlation of standard deviation and arithmetic average.

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