9. MEASURES OF CENTRAL TENDENCY CENTRAL TENDENCY Aggregate/ Sum of the multiple Observations divided by no. of observations is mean value. The mid point value of an arranged no. of observations The most frequently occurring Value in the Observation.
25. 1. Measures the scattering / variability of data around a measure of CT. 2. Gives an idea about the homogeneity or heterogeneity of the distribution of data. : Range, Mean Deviation (MD), Standard Deviation (SD), Quartile Deviation (QD) Coefficients of range, Coefficient of Range: [L-S]/[L+S. Co-efficient of MD Coefficient of MD = MD/M (Where M = Mean/ Median) MEASURES OF DISPERSION/VARIATIONS 1 Absolute Measures Relative Measures:
27. NORMAL STATISTICAL CURVE 68% 95% 99.7% Mean – 0 Total Area – 1 SD-1 SD-2 SD-3 In 95% confidence level there is probability of 5% of the data is outside SD-2 i.e. 1 in 20 samples therefore the probability P = 5/100 = 1/20 = 0.05 1 CT
31. INTERPRETATION (STANDARD ERROR) Standard Error is a measure which enables to judge whether the mean of a given sample is within the set confidence level of population mean or not. STANDARD ERROR STANDARD ERROR OF MEAN STANDARD ERROR BETWEEN TWO MEANS STANDARD ERROR OF PROPORTION STANDARD ERROR OF DIFFERENCE BETWEEN TWO PROPORTION CHI- SQUARE TEST
33. EXAMPLE Take Random Sample of 25 males of age 12 years Mean Height is 50” and SD of 0.6 S.E of mean = SD/ √ (n) [n = Total Sample] = 0.6/ √25 = 0.6/5 = 0.12 at 95% confidence level = 50” ± (2x 0.12) = 50” ± 0.24 = 49.76 to 50.24 i.e. the population mean chance is 1 in 20 out side these limits.
34. Standard Error of proportion: p = Proportion of Male = 52 q = Proportion of Female = 48 n = Size of the sample = 100 In random sample of 100 the proportion of Male is 40 while in the population male is 62 Relative Deviate – 52- 40 = 2.4 which is more than 2 hence the deviation is significant. SE (P) = √ pq n √ 52 X 48 100 = √ 2496 100 = √ 24.96 = 5 52 + 2 (5) = 62 52- 2 (5) = 42 5
36. Regression: It measures back wards and study of relation in cause and effect is possible between two dependable or independent variables. Given the value of independent variable, value of the dependent variable can be obtained by the formula y = y + b (x- x) Regression co- efficient (b) can be calculated as for Y upon ‘X’ b = ∑ (x- xi) (y- yi) ∑ (x-xi) 2
38. SAMPLING METHODS Random Sampling Non Random Sampling Simple Restricted Judgment Convenience (When no of unit are less) (Easy to approach) Systematic Stratified Multistage
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