STAT 113 Week 5 (Feb 4)
Work Sheet 3 key: Chapter 16 & 10
 Categorical or Quantitative variables with Graphs
1. In an internet poll from quibblo.com 629 respondents indicated the following as
their favorite Harry Potter character. Find the percents for Severus rounded to the
nearest ones-place. What kind of graph (among bar graph, pie chart and line graph)
would be most appropriate to represent this data?
Favorite Harry Potter Character Count
Percent
Hermione
164
26%
Harry
129
21%
The Dark Lord
43
7%
Dumbledore
52
8%
241
38%
Severus
A pie chart can show how the whole is divided into parts with the percentages, but
one could also make a bar graph to represent this data.
2. We want to know the distribution of people’s favorite animals if they are allowed
to choose more than one animal. Is this variable categorical or quantitative? What
kind of graph (among bar graph, pie chart and line graph) would be most
appropriate to represent this variable?
Categorical, we can use a bar graph but not pie chart since they are allowed to give
more than one answer.
3. The price of Coca Cola has been changing over the years. Is this variable
categorical or quantitative? Please make a graph to display the data below.
59
1973
69
1974
88
1982
99
90
1968
80
81
70
1964
60
of Coke (cents)
100
Price for a six pack
price for a 6 pack of Coke (cents)
Year
1965
1970
1975
Years
Quantitative
1980
 The Consumer Price and Index (CPI) and Government Statistics
4. Harvard charged $5900 for tuition, room, and board in 1976. The 2007 charge was
$42,078. The CPI for 1976 was 56.9, and the CPI for 2007 was 207.3. Express
Harvard's 1976 charges in 2007 dollars.
CPI at 2007
Dollars at 2007=CPI at 1976 × Dollars at 1976 =
207.3
× 5900 = 21495.08
56.9
5. An out-of-state Purdue undergraduate education costs $20,000 a year in 2000.
Calculate the “Tuition index number” in 2008 using 2000 as the base (2000 =
100), if the out-of-state tuition was $30000 in 2008.
Index =
value
30000
× 100 = 20000 × 100 = 150
base value
6. A food faddist eats only steak, rice, and ice cream. In 1995, he bought:
Item
1995 Quantity
1995 Price
Steak
200 pounds
$5.45/pound
Rice
300 pounds
$0.49/pound
Ice Cream
50 gallons
$5.08/gallon
After a visit from his mother, he adds oranges to his diet. Oranges cost $0.56/pound in
1995. Here are the food faddist's food purchases in 2005:
Item
2005 Quantity
2005 Price
Steak
175 pounds
$6.89/pound
Rice
325 pounds
$0.55/pound
Ice Cream
50 gallons
$6.69/gallon
Oranges
100 pounds
$0.63/pound
Find the fixed market basket Food Faddist Price Index (1995 = 100) for the year
2005.
Item
1995
Quantity
1995 Price
1995 Cost
2005 Price
2005 Cost
Steak
200 pounds
$5.45/pound
$1090
$6.89/pound
$1378
Rice
300 pounds
$0.49/pound
$147
$0.55/pound
$165
Ice Cream
50 gallons
$5.08/gallon
$254
$6.69/gallon
$334.5
Oranges
0
$0.56
$0
$0.63/pound
$0
Total
$1491
$1877.50
value
Index = base value × 100 =
1877.5
1491
× 100 =125.92