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Unformatted text preview: Statistics 309- chapter 1 I. Mean and Median A. The mean uses the actual value of each observation and so will chase a single small observation downward. B. The mean and median of symmetric distribution are close together C. If the mean and median are exactly symmetric, the mean and median are exactly the same D. In a skewed distribution, the mean is farther out in the long tail in the long tail than is the median I I. Quartiles: measuring spread A. The simplest useful numerical description of a distribution consists of both a measure of center and a measure of spread B. One way to measure spread is to gove the smallest and largest observations C. The pth percentile of a distribution is the value such that p percent of the observations fall at or below it. D. The median is just the 50 th percentile, so the use of percentiles to report spread is particularly appropriate when the median is our measure of center E. The first quartile is the 25 th percentile, and the third quartile is the 75 th percentile. that is, the first and third quartiles show the spread of the middle half of the data F. The second quartile is the median itself G. To calculate quartiles: 1. Arrange the observations in increasing order and llocate the median in the ordered list of observations 2. The first quartile is the median of the observations whose position in the ordered list is to the left of the location of the overall median 3. The third quartile is the median of the observations whose position in the ordered list is to the right of the location of the overall median H. The five number summary 1. A five number summary of a distribution consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest. 2. A boxplot is a graph of the five number summary a. A central box spans the quartiles b. A line in the box marks the median c. Lines extend from the box out to the smallest and largest observations I I I.Measuring spread: the standard deviation I I I....
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- Spring '09