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