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# Be a pro in statistics

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### Be a pro in statistics

1. 1. Presentation on Measures of Central tendency and Dispersion2/8/2012 Business Statistics 1
2. 2. CENTRAL TENDENCY • Middle point of distribution • Middle point at which the distribution is in balance • Why it is necessary? • Central tendency gives us simple and brief description of the main features of the whole data. • The measures of central tendency or averages reduce the data to a single value which is highly useful for making comparison. • Eg. Marks obtained by a student in a class2/8/2012 Business Statistics 2
3. 3. MEASURES OF CENTRAL TENDENCY MEAN CENTRAL TENDENCY MODE MEDIAN2/8/2012 Business Statistics 3
4. 4. DISPERSION• Spread of data in the distribution• To find out how far the variable is spread out in a distribution• Why it is necessary? • To analyze variability and uncertainty • Observations are nearer to center- dispersion/scatter/variation- small • Observations are farther to center- dispersion/scatter/variation- high Eg. Random Experiment conducted in physics for measuring the error of an equipment. 2/8/2012 Business Statistics 4
5. 5. MEASURES OF DISPERSION RANGE STANDARD DEVIATION DISPERSION VARIANCE2/8/2012 Business Statistics 5
6. 6. SKEWNESS & KURTOSIS IN DISPERSION • Distribution curves- symmetric or skewed • Skewness- concentration of values on 1 side • Mean<median<mode. • Positively/Right skewed- tailing off towards right • Negatively/Left skewed- tailing off towards left • Kurtosis- peakedness, how sharp the curve is which in turn determines how less the variations are. • K>3 Leptokurtic; K=3Mesokurtic; K<3Platykurtic2/8/2012 Business Statistics 6
7. 7. SKEWNESS2/8/2012 Business Statistics 7
8. 8. KURTOSIS2/8/2012 Business Statistics 8
9. 9. MEAN • ARITHMETIC MEAN • WEIGHTED MEAN • GEOMETRIC MEAN• Useful when unique value is required for decision making• Disadvantageous when large set of data needs to be analyzed2/8/2012 Business Statistics 9
10. 10. MEDIAN & MODE• Median- Middle most observation • Grouped and ungrouped data• Mode- the value that is most repeated in the dataset• Disadvantages of both- not affected by extreme values.2/8/2012 Business Statistics 10
11. 11. MEDIAN• EXAMPLE2/8/2012 Business Statistics 11
12. 12. MEASURES OF DISPERSION• RANGE • INTERFRACTILE RANGE • INTERQUARTILE RANGE• STANDARD DEVIATION• VARIANCE• COEFFICIENT OF VARIATION- Standard deviation as a percentage of mean.2/8/2012 Business Statistics 12
13. 13. Use of Standard Deviation• Example:• An IQ test- Normally distributed-with a mean of 100 and σ of 15. • About what % of people have IQ scores A)above 100; B)above 145 C) below 85.• Answer: • Use 68-95-99.7 rule. • 68% of the area in the curve- in 1*σ range • 95% of the area in the curve- in 2*σ range • 99.7% of the area in the curve- in 3*σ range.2/8/2012 Business Statistics 13
14. 14. BINOMIAL DISTRIBUTION• Used to model the number of successREQUIREMENTS• ‘n’ repeated identical independent trials• Only 2 outcomes (success/failure)• P(success)= p• P(failure)=q• Provided p+q=1• P(x) = The probability that there will be exactly ‘x’ successes in ‘n’ trials given by • P(x)= (n!/(n-x)!x!) *p^x*q^(n-x) 2/8/2012 Business Statistics 14
15. 15. BINOMIAL DISTRIBUTION Example: • In an exam with multiple choice- 10 questions-5 choices (a,b,c,d,e)- what is the probability u get exactly 4 questions correct just by guessing. • Answer: 0.09~= 9% P(S)=0.5=p, P(F)=0.8=q. N=10; x=4; • Use P(x) = The probability that there will be exactly ‘x’ successes in ‘n’ trials given by • P(x)= (n!/(n-x)!x!) *p^x*q^(n-x)2/8/2012 Business Statistics 15
16. 16. 2/8/2012 Business Statistics 16