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Homework Assignment 3

The following table shows heights of US presidents. The data is already sorted for you. Also for your convenience, the mean and standard deviation of the data are 179.81 and 6.875, respectively. Notice that since all presidents are included in the table, the data represents a population __ not a sample.

  1. Plot a box-and-whisker plot (box plot) representing presidents’ heights. On your graph, clearly label  the Min, Max, Q1, Q2, Q3, and the Median. Interpret your graph.
  2. According to Chebyshev’s theorem, what’s the minimum percentage of presidents that fall within 1.5 standard deviations from the mean? According to the data, what percentage of presidents actually falls within this interval?
  3. Assuming the distribution of presidential heights is bell-shaped, what percentage of presidents should fall within  the interval (172.935 , 186.685) ? What percentage of presidents actually falls within this interval?
  4. Calculate Z scores for Abraham Lincoln, Dwight D. Eisenhower, and James Madison. Interpret each of these scores.
PresidentHeight (cm)
Abraham Lincoln193
Lyndon B. Johnson192
Thomas Jefferson189
George Washington188
Chester A. Arthur188
Franklin D. Roosevelt188
George H. W. Bush188
Bill Clinton188
Andrew Jackson185
Ronald Reagan185
Barack Obama185
James Monroe183
John Tyler183
James Buchanan183
James A. Garfield183
Warren G. Harding183
John F. Kennedy183
Gerald Ford183
William Howard Taft182
Herbert Hoover182
Richard Nixon182
George W. Bush182
Grover Cleveland180
Woodrow Wilson180
Dwight D. Eisenhower179
Franklin Pierce178
Andrew Johnson178
Theodore Roosevelt178
Calvin Coolidge178
Jimmy Carter177
Millard Fillmore175
Harry S. Truman175
Rutherford B. Hayes174
William Henry Harrison173
James K. Polk173
Zachary Taylor173
Ulysses S. Grant173
John Quincy Adams171
John Adams170
William McKinley170
Benjamin Harrison168
Martin Van Buren168
James Madison163

 

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