2.1A D ESCRIBING L OCATION IN A D ISTRIBUTION  Using percentiles  Making an Ogive  Calculating and Interpreting a z -score.

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Presentation transcript:

2.1A D ESCRIBING L OCATION IN A D ISTRIBUTION  Using percentiles  Making an Ogive  Calculating and Interpreting a z -score

What is a percentile?

Wins in Major League Baseball The stemplot below shows the number of wins for each of the 30 Major League Baseball teams in Key: 5|9 represents a team with 59 wins

Key: 5|9 represents a team with 59 wins. Calculate and interpret the percentiles for the Colorado Rockies (92 wins), the New York Yankees (103 wins) and the Cleveland Indians (65 wins)

Ogive?

Age of Senators in the 103 rd Congress (n=100) FreqRel FreqCumul. Rel. Freq 30 −< −< −< −< −< −<

Age of Senators in the 103 rd Congress (n=100) FreqRel FreqCumul. Rel. Freq 30 −< −< −< −< −< −<

Age of Representatives in the 103 rd Congress (n=435) FreqRel FreqCumul. Rel. Freq 30 −< −< −< −< −< −< 903

State Median Household Incomes Below is a cumulative relative frequency graph showing the distribution of median household incomes for the 50 states and the District of Columbia.

a)California, with a median household income of $57,445, is at what percentile? Interpret this value.

b) What is the 25 th percentile for this distribution? What is another name for this value?

c)Where is the graph the steepest? What does this indicate about the distribution?

z-score?

Macy, a 3-year-old female is 100 cm tall. Brody, her 12-year-old brother is 158 cm tall. Obviously, Brody is taller than Macy—but who is taller, relatively speaking? That is, relative to other kids of the same ages, who is taller? (According to the CDCP, the heights of three-year-old females have a mean of 94.5 cm and a standard deviation of 4 cm. The mean height for 12-year-olds males is 149 cm with a standard deviation of 8 cm.)

YearPlayerHRMeanSD 1927Babe Ruth Roger Maris Mark McGwire Barry Bonds To make a fair comparison, we should see how these performances rate relative to others hitters during the same year. Calculate the standardized score for each player and compare.

YearPlayerHRMeanSD 1927Babe Ruth Roger Maris Mark McGwire Barry Bonds In 2001, Arizona Diamondback Mark Grace’s home run total had a standardized score of z = –0.48. Interpret this value and calculate the number of home runs he hit.