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1.
If a class of 27 students had a mean of 72 on a test, interpret the mean of 72 in the sense of a fair share measure of
the center of the test scores.
2. Suppose that your school's soccer team has scored a mean of 2 goals in each of 5 games.
a.
Draw a representation using cubes that displays that your school's soccer team has scored a mean of 2 goals in
each of 5 games. Let 1 cube stand for 1 goal.
b. Draw a dot plot that displays that your school's soccer team has scored a mean of 2 goals in each of 5 games.

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Solution

1. Interpretation of the Mean of 72 in the Test Scores
- Mean of 72 Interpretation:
- A mean score of 72 across a class of 27 students indicates that the average score of the students is 72. In other words, if the total sum of all students' test scores was evenly distributed, each student would have a score of 72. This 'fair share' measure reflects the central value around which the individual students' scores are distributed.

2. Representation of Soccer Team's Goals
- Suppose the school's soccer team has scored a mean of 2 goals in each of 5 games.

a. Representation Using Cubes:
- To represent this, you would use cubes where each cube corresponds to 1 goal. Since there were 2 goals per game over 5 games, the total number of goals scored is \(\( 2 \times 5 = 10 \)\) goals.
- Hence, a representation using cubes would consist of 10 cubes.

- Number of Cubes:
- [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
- This list represents 10 cubes, each representing 1 goal, demonstrating that the team scored 10 goals in total across 5 games.

b. Dot Plot Representation:
- A dot plot is another way to show the distribution of the scores. Here, you would illustrate with dots how many goals were scored in each game.
- In this case, since the team scored exactly 2 goals in each of the 5 games, your dot plot would look like this:

\(\[ \begin{align*} \text{Game 1:} & \quad \cdot\ \cdot \\ \text{Game 2:} & \quad \cdot\ \cdot \\ \text{Game 3:} & \quad \cdot\ \cdot \\ \text{Game 4:} & \quad \cdot\ \cdot \\ \text{Game 5:} & \quad \cdot\ \cdot \\ \end{align*} \]\)

- Dot Plot Structure:
- This dot plot shows that in each game from 1 to 5, the team scored 2 goals. This can also be represented in a dictionary format where each game number maps to the number of goals scored:

- {1: 2, 2: 2, 3: 2, 4: 2, 5: 2}

### Summary

- For the test scores: the mean of 72 represents the average score if scores were evenly distributed among 27 students.
- For the soccer team:
- Cube Representation:
- 10 cubes, as each cube stands for 1 goal, showing the total of 10 goals.
- Dot Plot Representation:
- Each game having exactly 2 goals in a dot plot format aligning from game 1 to game 5.

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