ECONOMICS 521 ECONOMIC STATISTICS

Jerry S. Kelly 312 Maxwell Hall (Not Eggers)

Sample Population Frequency distribution Probability distribution Descriptive Statistics Probability Theory Sample statistics Parameters Sampling distribution Inferential Statistics

Sample: x 1, x 2,..., x N (x 1, y 1 ), (x 2, y 2 ),..., (x N, y N ) Statistic: A function f(x 1, x 2,..., x N ) from samples to the real numbers

Measures of central tendency A statistic is a measure of central tendency if and only if (1) f(x 1 +A, x 2 +A,..., x N +A) = f(x 1, x 2,..., x N ) + A; and (2) f(Bx 1, Bx 2,..., Bx N ) = Bf(x 1, x 2,..., x N ).

Measures of Variation A statistic is a measure of variation if and only if (1) f(x 1 +A, x 2 +A,..., x N +A) = f(x 1, x 2,..., x N ); and (2) f(Bx 1, Bx 2,..., Bx N ) = *B*f(x 1, x 2,..., x N ).

1. f(x 1, x 2,..., x N ) = x 1 ; 2. f(x 1, x 2,..., x N ) = x 1 + x 2 ; 3. f(x 1, x 2,..., x N ) = (x 1 + x 2 )/2; 4. f(x 1, x 2,..., x N ) = x MAX ;

5. f(x 1, x 2,..., x N ) = (x MAX + x MIN )/2; 6. f(x 1, x 2,..., x N ) = (x 1 + x x N )/N = Mean 7. f(x 1, x 2,..., x N ) = Mode {x 1, x 2,..., x N }; 8. f(x 1, x 2,..., x N ) = Median {x 1, x 2,..., x N };

9. f(x 1, x 2,..., x N ) = * x 2 - x 1 * ; 10. f(x 1, x 2,..., x N ) = x MAX - x MIN