Section 6.1 - Investigating Relationships

1.

Elan drew a scatter of the data below. Most likely, why did Elan choose Weight as the independent variable

Because the weight is determined by the carat price

Because per carat price is based on its weight

Because weight is usually the independent variable

Because the weights are less than the prices

Elan most likely chose Weight as the independent variable because the per carat price is based on its weight. This suggests that the weight of the data points has a significant impact on determining the price per carat. Therefore, by choosing weight as the independent variable, Elan can analyze the relationship between weight and price more accurately.

Explanation

Elan most likely chose Weight as the independent variable because the per carat price is based on its weight. This suggests that the weight of the data points has a significant impact on determining the price per carat. Therefore, by choosing weight as the independent variable, Elan can analyze the relationship between weight and price more accurately.

2. Suppose you were to survey shoppers to see if there was a relationship between the number of coupons they use and the amount of money they spend. What column headings would you use in a table of values designed to organize the data from your survey?

Number of Coupons and Amount Saved

Number of Coupons and Amount Spent

Coupons Cut and Amount Spent

Amount Spent and Amount Saved

The column headings "Number of Coupons" and "Amount Spent" would be used in a table of values to organize the data from the survey. This is because the survey is trying to determine if there is a relationship between the number of coupons used and the amount of money spent by shoppers. By recording the number of coupons and the corresponding amount spent for each shopper, the data can be analyzed to determine if there is a correlation between these two variables.

Explanation

The column headings "Number of Coupons" and "Amount Spent" would be used in a table of values to organize the data from the survey. This is because the survey is trying to determine if there is a relationship between the number of coupons used and the amount of money spent by shoppers. By recording the number of coupons and the corresponding amount spent for each shopper, the data can be analyzed to determine if there is a correlation between these two variables.

3.

The scatter plot shows movie attendance at the Stadium Cinema for different days in the summer. What information does point R represent?

On a day when the temperature was 30 C, 400 tickets were sold

On a day when the temperature was 20 C, 261 tickets were sold

On a day when the temperature was 95 C, 602 tickets were sold

On a day when the temperature was 32 C, 420 tickets were sold

Point R on the scatter plot represents the day when the temperature was 32°C and 420 tickets were sold at the Stadium Cinema.

Explanation

Point R on the scatter plot represents the day when the temperature was 32°C and 420 tickets were sold at the Stadium Cinema.

4.

For the scatter plot above, which is the independent variable?

Volume

Pumping Rate

Fountain Type

Time

The independent variable in a scatter plot is the variable that is manipulated or controlled by the experimenter. In this case, the scatter plot does not provide any information about how the other variables (Volume, Pumping Rate, and Fountain Type) are related or influenced by each other. However, it is likely that the Time variable represents the independent variable as it is often used to measure the progression or duration of an experiment or observation.

Explanation

The independent variable in a scatter plot is the variable that is manipulated or controlled by the experimenter. In this case, the scatter plot does not provide any information about how the other variables (Volume, Pumping Rate, and Fountain Type) are related or influenced by each other. However, it is likely that the Time variable represents the independent variable as it is often used to measure the progression or duration of an experiment or observation.

5. The hockey team practices 10 hours per week. Suppose you were to survey your teamates to see if there is a relationship between extra hours spend practicing and number of goals made. How would you interpret the ordered pair (3, 12) if it were to appear on a scatter plot of your data?

A player practicing 12 extra hours and scoring 3 extra goals

A player practicing 2 extra hours and scoring 3 goals

A player practicing 3 extra hours and scoring 12 goals

A player practicing 13 extra hours and scoring 12 goals

The ordered pair (3, 12) represents a player who practices 3 extra hours and scores 12 goals. This suggests that there is a positive relationship between the number of extra hours spent practicing and the number of goals made. As the player increases their practice time by 3 hours, their goal count increases by 12.

Explanation

The ordered pair (3, 12) represents a player who practices 3 extra hours and scores 12 goals. This suggests that there is a positive relationship between the number of extra hours spent practicing and the number of goals made. As the player increases their practice time by 3 hours, their goal count increases by 12.

6.

The data shoes the daily low temperatures in Banff National Park for the part of July. How would you describe the variables?

Discrete

Continuous

Independent

Dependent

The variables in this case are discrete because they represent specific values of daily low temperatures in Banff National Park for a specific part of July. Discrete variables are those that can only take on specific, separate values and cannot be measured on a continuous scale. In this case, the daily low temperatures can only be specific values and cannot be measured as a continuous range.

Explanation

The variables in this case are discrete because they represent specific values of daily low temperatures in Banff National Park for a specific part of July. Discrete variables are those that can only take on specific, separate values and cannot be measured on a continuous scale. In this case, the daily low temperatures can only be specific values and cannot be measured as a continuous range.

7.

This data shows the fuel consumption for various vehicles of different weights. Who might want this information

An auto manufacturer

An oil company executive

A vehicle designer

A scrap metal dealer

A vehicle designer would want this information in order to understand the fuel consumption of vehicles with different weights. This would help them in designing more fuel-efficient vehicles and optimizing the weight distribution to improve fuel efficiency.

Explanation

A vehicle designer would want this information in order to understand the fuel consumption of vehicles with different weights. This would help them in designing more fuel-efficient vehicles and optimizing the weight distribution to improve fuel efficiency.

8.

For the data shown above, which is the dependent variable?

Jump Distance

Years

1948

Olympic Gold Medals

The dependent variable in this scenario is the Jump Distance. The dependent variable is the one that is being measured or observed and is expected to change in response to the independent variable. In this case, the independent variable is not provided, but it can be assumed that the Jump Distance is being measured and observed based on some other factor or factors.

Explanation

The dependent variable in this scenario is the Jump Distance. The dependent variable is the one that is being measured or observed and is expected to change in response to the independent variable. In this case, the independent variable is not provided, but it can be assumed that the Jump Distance is being measured and observed based on some other factor or factors.

9.

The table above shows the number of laps Craig swam during practice. How would you join the points on the scatter plot of this data?

Dashed because they are discrete

Solid because they are discrete

Dashed because they are continuous

Solid because they are continuous

The points on the scatter plot should be joined with dashed lines because the data points represent discrete values. Discrete data refers to values that are separate and distinct, such as the number of laps Craig swam during practice. Dashed lines are commonly used in scatter plots to indicate that the data points are not connected in a continuous manner.

Explanation

The points on the scatter plot should be joined with dashed lines because the data points represent discrete values. Discrete data refers to values that are separate and distinct, such as the number of laps Craig swam during practice. Dashed lines are commonly used in scatter plots to indicate that the data points are not connected in a continuous manner.

10.

What does the scatter plot show about the relationship between the amount spent per pupil and the average teacher pay?

There is no relationship between amount spent per pupil and teacher salary.

Schools the spend more per pupil tend to pay their teachers less per year

Schools that spend more per pupil tend to pay their teachers more per year

Schools that pay their teachers more per year tend to spend less per pupil

The scatter plot shows a positive relationship between the amount spent per pupil and the average teacher pay. This means that as the amount spent per pupil increases, the average teacher pay also tends to increase.

Explanation

The scatter plot shows a positive relationship between the amount spent per pupil and the average teacher pay. This means that as the amount spent per pupil increases, the average teacher pay also tends to increase.