资讯四个领域.pptVIP

Summary Measures Chapter Topics Measures of central tendency, variation, and shape Mean, median, mode, geometric mean Quartiles Range, interquartile range, variance and standard deviation, coefficient of variation, Z-scores Symmetric and skewed distributions Population summary measures Mean, variance, and standard deviation The empirical rule and Chebyshev rule Measures of Central Tendency Arithmetic Mean The arithmetic mean (mean) is the most common measure of central tendency For a sample of size n: Arithmetic Mean The most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers) Numerical Measures for a Population Population summary measures are called parameters The population mean is the sum of the values in the population divided by the population size, N Median In an ordered array, the median is the “middle” number (50% above, 50% below) Not affected by extreme values Finding the Median The location of the median: If the number of values is odd, the median is the middle number If the number of values is even, the median is the average of the two middle numbers Note that is not the value of the median, only the position of the median in the ranked data Mode A measure of central tendency Value that occurs most often Not affected by extreme values Used for either numerical or categorical (nominal) data There may be no mode There may be several modes Example: The Crash of 1987 Dow-Jones Industrials, stock-price changes as each stock began trading that fateful morning Fairly normal相當正常 Mean and median are similar Example: Incomes Personal income of 100 people Average is higher than median due to skewness Example: Review Example:Summary Statistics Geometric Mean Geometric mean Used to measure the rate of change of a variable over time Geometric mean rate of return Measures the status of an investment over time Where Ri is the rate of return in time period i Example