https://file.aiquickdraw.com/mathbot/file/1729626443986kjagz8j5.jpg

The problem is asking for the total number of home and away games played, using the given mean values for goals.

### Given:
- The **mean number of home goals** is **1.5**.
- The **mean number of away goals** is **2.5**.
- The chart provides the **total goals** scored in each of the 4 quarters.

Let's calculate the total goals scored from the chart and use the means to find the number of games played.

#### 1. Home Goals (blue bars):
- 1st quarter: 2 goals
- 2nd quarter: 8 goals
- 3rd quarter: 3 goals
- 4th quarter: 6 goals
  - **Total home goals = 2 + 8 + 3 + 6 = 19 goals**

#### 2. Away Goals (green bars):
- 1st quarter: 6 goals
- 2nd quarter: 4 goals
- 3rd quarter: 7 goals
- 4th quarter: 5 goals
  - **Total away goals = 6 + 4 + 7 + 5 = 22 goals**

### Step 1: Find the number of home games
Since the mean number of home goals is 1.5:
\[
\text{Total home games} = \frac{\text{Total home goals}}{\text{Mean home goals}} = \frac{19}{1.5} = \frac{38}{3} \approx 12.67
\]
Rounding this value gives **13 home games**.

### Step 2: Find the number of away games
Since the mean number of away goals is 2.5:
\[
\text{Total away games} = \frac{\text{Total away goals}}{\text{Mean away goals}} = \frac{22}{2.5} = 8.8
\]
Rounding this value gives **9 away games**.

### Step 3: Total number of games
\[
\text{Total games} = 13 \text{ home games} + 9 \text{ away games} = 22 \text{ games in total}.
\]

Therefore, the total number of home and away games played is **22**.

Would you like any additional details on the steps? Here are some follow-up questions:

1. How do we calculate a mean from a given set of data?
2. Why do we round the number of games in this case?
3. Could the mean goals scored per game vary depending on more data?
4. How do you calculate the total goals based on a frequency chart like this one?
5. Why is it important to distinguish between home and away games in sports statistics?

**Tip:** When working with mean values, always check if rounding is appropriate depending on the context of the problem.

Here is some information about the goals scored in some hockey games. Each game has four quarters. The mean number of home goals scored is 1.5, and the mean number of away goals scored is 2.5. How many home and away games have been played in total?

Learn how to calculate the total number of hockey games played based on the mean number of home and away goals. The problem involves calculating averages and interpreting a bar graph. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation