Using R for Introductory Statistics : John Verzani

Univariate data 532.13 Can you copyedit this paragraph from the August 16, 2003 New York Times?The median sales price, which increased to $575,000, almost 12 per-centmore than the median for the previous quarter and almost 13 percent morethan the median for the period a year ago, was at its highest level since thefirst market overview report was issued in 1989. (The median price ismidway between the highest and lowest prices.)2.14 In real estate articles the median is often used to describe the center, as opposed tothe mean. To see why, consider this example from the August 16, 2003 New York Timeson apartment prices:The average and the median sales prices of cooperative apartments wereat record highs, with the average up almost 9 percent to $775,052 from thefirst quarter this year, and the median price at $479,000, also an increaseof almost 9 percent.Explain how using the median might affect the reader’s sense of the center.2.15 The data set pi2000 (UsingR) contains the first 2,000 digits of π. What is thepercentage of digits that are 3 or less? What percentage of the digits are 5 or more?2.16 The data set rivers contains the lengths (in miles) of 141 major rivers in NorthAmerica.1. What proportion are less than 500 miles long?2. What proportion are less than the mean length?3. What is the 0.75 quantile?2.17 The time variable in the nym. 2002 (UsingR) data set contains the time to finishthe 2002 New York City marathon for a random sample of the finishers.1. What percent ran the race in under 3 hours?2. What is the time cutoff for the top 10%? The top 25%?3. What time cuts off the bottom 10%?Do you expect this data set to be symmetrically distributed?2.18 Compare values of the mean, median, and 25% trimmed mean on the built-inrivers data set. Is there a big difference among the three?