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05:54
04:39
06:38Extending Concepts
Golf The distances (in yards) for nine holes of a golf course are listed.
336 393 408 522 147 504 177 375 360
d. Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.
Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown.
d. Can you determine which concert lasted longer? Explain.
Pearson’s Index of Skewness The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.
P = 3 (x̄ - median) / s
Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.
e. x̄ = 155, s = 20.0, median = 175
Pearson’s Index of Skewness The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.
P = 3 (x̄ - median) / s
Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.
c. x̄ = 9.2, s = 1.8, median = 9.2
Use the frequency histogram
describe any patterns with the data..
