http://www.ck12.org Chapter 2. Visualizations of Data
- If the median of a distribution is less than the mean, which of the following statements is the most correct?
a. The distribution is skewed left.
b. The distribution is skewed right.
c. There are outliers on the left side.
d. There are outliers on the right side.
e. b or d could be true. - The following table contains recent data on the average price of a gallon of gasoline for states that share a
border crossing into Canada.
a. Find the five-number summary for this data.
b. Show all work to test for outliers.
c. Graph the box-and-whisker plot for this data.
d. Canadian gasoline is sold in liters. Suppose a Canadian crossed the border into one of these states and
wanted to compare the cost of gasoline. There are approximately 4 liters in a gallon. If we were to
convert the distribution to liters, describe the resulting shape, center, and spread of the new distribution.
e. Complete the following table. Convert to cost per liter by dividing by 3.7854 and then graph the resulting
box plot.
As an interesting extension to this problem, you could look up the current data and compare that distribution with
the data presented here. You could also find the exchange rate for Canadian dollars and convert the prices into the
other currency.
TABLE2.30:
State Average Price of a Gallon of Gaso-
line(US$)Average Price of a Liter of Gasoline
(US$)
Alaska 3. 458
Washington 3. 528
Idaho 3. 26
Montana 3. 22
North Dakota 3. 282
Minnesota 3. 12
Michigan 3. 352
New York 3. 393
Vermont 3. 252
New Hampshire 3. 152
Maine 3. 309Average Prices of a Gallon of Gasoline on March 16, 2008
Figure:Average prices of a gallon of gasoline on March 16, 2008.Source:AAA, http://fuelgaugereport.opisnet.c
om/sbsavg.html
Review Answers
- (a) 35, 53 , 67. 5 , 75. 5 ,95 (b)
IQR= 22. 5.
1. 5 ∗IQR= 33. 75