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Unformatted text preview: Useful Formulas and Definitions Summary Statistics 1. Quantile/Percentile of Observation i = (Number of Obs i )/(Total Number of Obs) 2. Median: The smallest number A such that percentile( A ) . 5. 3. Lower Quartile: The 25 th quantile. 4. Upper Quartile: The 75 th quantile. 5. The Mode: The most frequent value in the sample. 6. The Mean: X = 1 n n i =1 X i 7. Range: (Largest Observation) - (Smallest Observation) 8. Interquartile Range (IQR) = (Upper Quartile) - (Lower Quartile) 9. Mean Absolute Deviation (MAD): 1 n n i =1 | X i- X | 10. Mean Squared Deviation (MSD): 1 n n i =1 ( X i- X ) 2 11. Sample Variance: s 2 X = 1 n- 1 n i =1 ( X i- X ) 2 12. Sample Standard Deviation: s X = q 1 n- 1 n i =1 ( X i- X ) 2 13. Linear transformations: Suppose Y i = a + bX i , then: (a) Y = 1 n n i =1 Y i = a + b X (b) s 2 Y = 1 n- 1 n i =1 ( Y i- Y ) 2 = b 2 s 2 X Random Variables 1. For Discrete Random Variables: (a) Probability Mass Function (pmf): p ( a ) = P ( X = a ). (b) Cumulative Distribution Function (cdf): F ( a ) = P ( X a ). (c) Mean: = xp ( x ) (d) Variance: 2 = ( x- ) 2 p ( x ) (e) Standard Deviation = p ( x- ) 2 p ( x ) 2. Binomial distribution: Let n be the number trials, let be the probability of success at each trial and s the number of successes. Then the pmf of a Binomial Distribution is given by p ( s ) = n !...
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This note was uploaded on 11/30/2010 for the course ECON 120A 1684210 taught by Professor Elliot during the Spring '10 term at UCSD.
- Spring '10