We are given a set of questions related to bivariate data. Question 1 asks about the association and real-world representation of a given scatter plot. Question 3 asks us to complete a two-way table. Question 4 asks us to find the percentage of 7th graders who do not have a pet. Question 5 requires us to draw a line of best fit on a scatter plot, determine its equation, and use it to predict a value.

1. Problem Description

We are given a set of questions related to bivariate data.

Question 1 asks about the association and real-world representation of a given scatter plot.

Question 3 asks us to complete a two-way table.

Question 4 asks us to find the percentage of 7th graders who do not have a pet.

Question 5 requires us to draw a line of best fit on a scatter plot, determine its equation, and use it to predict a value.

2. Solution Steps

Question 1:

The scatter plot shows a negative association. As the x-values increase, the y-values tend to decrease. A possible real-world situation could be the relationship between temperature and the number of ice cream sales. As the temperature increases, ice cream sales decrease because people go to the beach or swim at pools.

Question 3:

To complete the two-way table, we need to fill in the missing values.

First, we can calculate the number of 7th graders who own a dog.

Total 7th graders =

1

8

2. From the table, Cat + Other + No Pet = 58 + blank + blank. Therefore the value can be calculated from Total number of 7th graders - known values equals to dog owner, which equals $182-58-24-31 = 69$.

We can also compute the totals for each pet type.

The completed table is shown below:

| | Dog | Cat | Other | No Pet | Total |

| ----- | --- | --- | ----- | ------ | ----- |

| 6th | 76 | 19 | 30 | 90 | 215 |

| 7th | 69 | 58 | 24 | 31 | 182 |

| 8th | 88 | 24 | blank | blank | |

| Total | 251 | 194 | 50 |blank | |

Question 4:

From the completed table, the number of 7th graders who do not have a pet is

3

1. The total number of 7th graders is

1

8

2. The percentage of 7th graders who do not have a pet is:

$\frac{31}{182} \times 100 \approx 17.03\%$

Rounding to the nearest tenth, the percentage is 17.0%.

Question 5:

(a) Draw a line of best fit on the scatter plot. The line should roughly pass through the points (50, 20) and (200, 50).

(b) Determine the equation for the line of best fit.

The slope of the line is:

$m = \frac{50 - 20}{200 - 50} = \frac{30}{150} = 0.2$

Using the point-slope form with the point (50, 20):

$y - 20 = 0.2(x - 50)$

$y = 0.2x - 10 + 20$

$y = 0.2x + 10$

(c) Use the equation to predict the number of students who would join a club if there were 550 students in the school.

Substitute $x = 550$ into the equation:

$y = 0.2(550) + 10$

$y = 110 + 10$

$y = 120$

3. Final Answer

Question 1:

The scatter plot shows a negative association. A possible real-world situation could be the relationship between temperature and the number of ice cream sales.

Question 3:

| | Dog | Cat | Other | No Pet | Total |

| ----- | --- | --- | ----- | ------ | ----- |

| 6th | 76 | 76| 19 | 30 | 215 |

| 7th | 69 | 58 | 24 | 31 | 182 |

| 8th | 88 | 70+26 | 24 | 31 | 24 +24-167+366767 |

| Total | 251 | 194 | 50 | 92 | 7-17 |

Question 4:

17.0%

Question 5:

(a) A line of best fit is drawn on the scatter plot.

(b) The equation for the line of best fit is $y = 0.2x + 10$.

(c) If there were 550 students in the school, we predict 120 students would join a club.