MEASURES OF CENTRAL TENDENCY-Mean,median, mode.pptx

Measures of central tendency

1. Variables Constant and Variable Qualitative (Categorical) variable- 1.Ordinal 2. Nominal Quantitative (Measurable) variable- 1. Discrete 2. Continuous

2. MEASURES OF CENTRAL TENDENCY

3. The tendency of observations to cluster around a central value A single central value representative of the characteristics of entire data And to facilitate comparison

4. AVERAGES ---- 1. MATHEMATICAL arithmetic mean geometric mean harmonic mean 11. POSITIONAL median mode

5. Arithmetic mean x1+ x2 + x3 +……. x n n MERITS : Easy to calculate & understand Based on all observations, best representative Rigidly defined Capable of further statistical analysis

6. Income in Rs. / day of 7 people 50, 50, 50, 70, 100, 200, 1000 Mean=217.15

7. DEMERITS: Cannot be used for qualitative data Affected by extreme observations It may not be an observation in the data

8. Incubation period of a viral fever in 9 patients was found to be 14 13 11 15 10 7 9 12 10 Mean=

9. DBP NO: OF PATIENTS 60 4 61 5 65 5 70 4 80 10

10. ∑ f x ∑ f If class interval take x as mid value

11. Geometric mean nth √ x1* x2* x3*…… x n Used when the observations change exponentially, eg : no: of bacteria observed in an experiment at hourly intervals

12. Harmonic mean n/∑1/x Used in situations where the reciprocal values are considered for eg : the titres in serological studies like Widal Test

13. Median Arrange the data Value of middle observation In case of odd no: of observations; (N+1)/2th observation In case of even no: of observations; average of n/2 th and (n/2 +1) th observation

14. Income in Rs. / day of 7 people 50, 50, 50, 70, 100, 200, 1000 median = 70 more nearer to the truth MERITS: Easy to calculate Not affected by extreme values Can be determined graphically Can be used for skewed distribution

15. DEMERITS: Not based on all observations Cannot be used for further algebraic treatment Practical difficulty when data too large

16. Mode Most commonly/ frequently occuring value Easy to understand Not affected by extreme values Varies with sampling Cannot be used for further algebraic treatment If no observations are repeated…… If more than 1 observations are repeated……. Not often used

17. CALCULATE MEAN, MEDIAN & MODE Incubation period of a viral fever in 9 patients was found to be 14 13 11 15 10 7 9 12 10

18. THANK YOU DBP NO: OF PATIENTS 60 4 61 5 65 5 70 4 80 10