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Unformatted text preview: Study Guide for Economic Statistics Unit 0: Background Introduction to statistics (Section 1.1) Branches of statistics Descriptive statistics: presenting characteristics of a sample Inferential statistics: guessing properties of the population Vocabulary (Section 1.2) Population: group of interest to researcher Parameters: values in the population Sample: subset of population available to researcher Statistics: values calculated from the sample Observations: entities for which measurements are taken Variables: values differ between observations Quantitative variables: numerical values that measure Discrete: take on a limited set of values Continuous: take on any value from a range Qualitative variables: nonnumerical values (or not measuring) Categorical: each observation falls into exactly one group Ordered: a ranking (but no measurement) exists Nominal: no ranking exists Dummy variables: take values of 0 or 1 Noncategorical Econ 400 Study Guide, Fall 2011, p. 2 Unit 1: Descriptive Statistics (Chapters 1 & 2) Inherent tradeoff between precision and clarity Population parameters vs. sample statistics Techniques for univariate categorical data (Section 1.3) Frequency distributions Frequency distribution: number in each category Relative frequency distribution: fraction (percentage) of sample in each category Cumulative frequency distribution: fraction of sample at or below the category Bar graphs: visual presentation of frequency distribution Plain bar graph (numbers or percentages) Pareto diagram (percentages): superimposed cumulative frequency Component bar graph (usually numbers): bars divided into groups Clustered bar graph (often percentages): bars for groups presented sidebyside Pie graph (percentages): visual presentation of relative frequency distribution Numerical techniques for quantitative data Measures of central tendency in a sample: the “typical” observation (Section 2.1) (Arithmetic) Mean: the simple average, x = 1 n ∑ x i Median: the value in the middle Mode: the most frequent value Less common measures (Section 2.3) Geometric mean: x g = ∏ x i n (Weighted average) (Moving average) Econ 400 Study Guide, Fall 2011, p. 3 Symmetric vs. asymmetry; skewness Skewed to the left (negatively): distribution has a long tail to the left; values concentrated above the median; median above mean Skewed to the right (positively): distribution has a long tail to the right; values concentrated below the median; median below mean Measures of variability in a sample (Section 2.2) Range: difference between maximum and minimum Variance: s x 2 = 1 n − 1 ∑ ( x i − x ) 2 Units are the units of x , squared; not intuitive Standard deviation: s x = s x 2 Units are the units of x ; interpretable Tricks with standard deviations Relation to range: s x ≈ 1 4 Range Chebyshev’s theorem Twoway: At least (1 − 1 k 2 ) of the sample are within k standard deviations of mean....
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