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.
- 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.
- 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?
- 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?
- Calculate Z scores for Abraham Lincoln, Dwight D. Eisenhower, and James Madison. Interpret each of these scores.
| President | Height (cm) |
|---|---|
| Abraham Lincoln | 193 |
| Lyndon B. Johnson | 192 |
| Thomas Jefferson | 189 |
| George Washington | 188 |
| Chester A. Arthur | 188 |
| Franklin D. Roosevelt | 188 |
| George H. W. Bush | 188 |
| Bill Clinton | 188 |
| Andrew Jackson | 185 |
| Ronald Reagan | 185 |
| Barack Obama | 185 |
| James Monroe | 183 |
| John Tyler | 183 |
| James Buchanan | 183 |
| James A. Garfield | 183 |
| Warren G. Harding | 183 |
| John F. Kennedy | 183 |
| Gerald Ford | 183 |
| William Howard Taft | 182 |
| Herbert Hoover | 182 |
| Richard Nixon | 182 |
| George W. Bush | 182 |
| Grover Cleveland | 180 |
| Woodrow Wilson | 180 |
| Dwight D. Eisenhower | 179 |
| Franklin Pierce | 178 |
| Andrew Johnson | 178 |
| Theodore Roosevelt | 178 |
| Calvin Coolidge | 178 |
| Jimmy Carter | 177 |
| Millard Fillmore | 175 |
| Harry S. Truman | 175 |
| Rutherford B. Hayes | 174 |
| William Henry Harrison | 173 |
| James K. Polk | 173 |
| Zachary Taylor | 173 |
| Ulysses S. Grant | 173 |
| John Quincy Adams | 171 |
| John Adams | 170 |
| William McKinley | 170 |
| Benjamin Harrison | 168 |
| Martin Van Buren | 168 |
| James Madison | 163 |