Chapter Two Describing Location in a Distribution

 P ,3  P ,7

 Standardized Score (z-score) – number of standard deviation from mean  Percentile – the pth percentile of a distribution is the data value with p percent of the observations below it. There is no 100 th percentile.

 Jenny scored an 86 on a statistics test that had a mean of 80 and a standard deviation of She also scored an 82 on a chemistry test that had a mean of 76 and a standard deviation of four. She was six points the mean in each case.  Calculate her z-score for each test.  Relative to other members of the classes, which test did she do better on?

 Jenny’s score is the 22 nd highest of 25 scores counting from the lowest to the highest. What percentile is her score?

 The landmarks of baseball achievement are T Cobb’s batting average of.420 in 1911, Ted William’s.406 in 1941, and George Brett’s.390 in These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric, except for outliers such as Cobb, Williams, and Brett. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: Decade Mean Standard Deviation  1910s  1940s  1970S  Compute the standardized batting averages for Cobb, Williams, and Brett to compare how far each stood above his peers.

Number of Standard Deviations CalculationPercent of Data within this number of standard deviations of the mean 1standard deviation 2 standard deviations 3 standard deviations 4 standard deviations Make a Table Showing Results of Chebyshev’s Inequality