Question

ap stats lesson 1.1
homework

1. give two examples of quantitative variables and two examples of categorical variables.
2. a sports analyst collects information about all 30 major league baseball teams, recording which league (american league or national league), stadium capacity, number of wins last season, and whether or not the team reached the playoffs last season.

a. identify the individuals.
b. which variables are quantitative?
c. which variables are categorical?

1. the 481 top - grossing movies in a recent year were classified by the genre of the movie. the results are shown in the table.

genre of movie | drama | documentary | comedy | action | thriller | horror | other
frequency | 144 | 79 | 58 | 54 | 47 | 39 | 60
a. identify the variable. is it quantitative or categorical?
b. make a bar graph showing relative frequencies.
c. name another type of graph that could be used to display the data.

1. a cbs news survey asked a random sample of u.s. adults to identify their age and their preferred format for listening to music. the results are shown in the table.

a. identify the explanatory variable and the response variable.
b. what percent of all adults surveyed are 45 years or older and prefer listening to cds?
c. what percent of all adults surveyed prefer listening to the radio?
d. of those adults that prefer streaming, what percent are less than 45 years old?
math medic

Explanation:

1.

• Quantitative variables: Height (in inches) of students in a class, number of books in a library.
• Categorical variables: Eye - color (blue, brown, green etc.) of people, type of vehicle (car, truck, motorcycle) owned by individuals.

2.

• a. Individuals: Major league baseball teams
• b. Quantitative variables: Stadium capacity, number of wins last season
• c. Categorical variables: Whether or not the team reached the playoffs last season, which league (American League or National League)

3.

• a. Variable: Genre of movie. It is a categorical variable since movie genres are non - numerical categories.
• **b. First, calculate the relative frequencies:
• Total number of movies \(n = 144 + 79+58 + 54+47+39+60=481\)
• Relative frequency of Drama: \(\frac{144}{481}\approx0.30\)
• Relative frequency of Documentary: \(\frac{79}{481}\approx0.16\)
• Relative frequency of Comedy: \(\frac{58}{481}\approx0.12\)
• Relative frequency of Action: \(\frac{54}{481}\approx0.11\)
• Relative frequency of Thriller: \(\frac{47}{481}\approx0.10\)
• Relative frequency of Horror: \(\frac{39}{481}\approx0.08\)
• Relative frequency of Other: \(\frac{60}{481}\approx0.12\)
• Then, draw a bar graph with movie genres on the x - axis and relative frequencies on the y - axis.
• **c. A pie chart could also be used to display the data.

4.

• a. Explanatory variable: Age (Age < 45 or Age 45+). Response variable: Preferred listening format (streaming, radio, digital files, CDs)
• **b. Total number of adults surveyed \(=386 + 138+124 + 29+306+389+109+95=1576\)
• Number of adults 45 years or older and prefer CDs \( = 95\)
• Percentage \(=\frac{95}{1576}\times100\approx6.03\%\)
• **c. Number of adults who prefer radio \(=138 + 389=527\)
• Percentage \(=\frac{527}{1576}\times100\approx33.44\%\)
• **d. Number of adults who prefer streaming \(=386+306 = 692\)
• Number of adults who prefer streaming and are less than 45 years old \(=386\)
• Percentage \(=\frac{386}{692}\times100\approx55.8\%\)

Answer:

1.

• Quantitative variables: Height (in inches) of students in a class, number of books in a library.
• Categorical variables: Eye - color (blue, brown, green etc.) of people, type of vehicle (car, truck, motorcycle) owned by individuals.

2.

• a. Individuals: Major league baseball teams
• b. Quantitative variables: Stadium capacity, number of wins last season
• c. Categorical variables: Whether or not the team reached the playoffs last season, which league (American League or National League)

3.

• a. Variable: Genre of movie. It is a categorical variable since movie genres are non - numerical categories.
• **b. First, calculate the relative frequencies:
• Total number of movies \(n = 144 + 79+58 + 54+47+39+60=481\)
• Relative frequency of Drama: \(\frac{144}{481}\approx0.30\)
• Relative frequency of Documentary: \(\frac{79}{481}\approx0.16\)
• Relative frequency of Comedy: \(\frac{58}{481}\approx0.12\)
• Relative frequency of Action: \(\frac{54}{481}\approx0.11\)
• Relative frequency of Thriller: \(\frac{47}{481}\approx0.10\)
• Relative frequency of Horror: \(\frac{39}{481}\approx0.08\)
• Relative frequency of Other: \(\frac{60}{481}\approx0.12\)
• Then, draw a bar graph with movie genres on the x - axis and relative frequencies on the y - axis.
• **c. A pie chart could also be used to display the data.

4.

• a. Explanatory variable: Age (Age < 45 or Age 45+). Response variable: Preferred listening format (streaming, radio, digital files, CDs)
• **b. Total number of adults surveyed \(=386 + 138+124 + 29+306+389+109+95=1576\)
• Number of adults 45 years or older and prefer CDs \( = 95\)
• Percentage \(=\frac{95}{1576}\times100\approx6.03\%\)
• **c. Number of adults who prefer radio \(=138 + 389=527\)
• Percentage \(=\frac{527}{1576}\times100\approx33.44\%\)
• **d. Number of adults who prefer streaming \(=386+306 = 692\)
• Number of adults who prefer streaming and are less than 45 years old \(=386\)
• Percentage \(=\frac{386}{692}\times100\approx55.8\%\)