Calculate Mean Goals: Manchester United's 5-Match Scoring Analysis

Q: Why do I need to add up all the goals first?

The mean (average) requires the total sum! You can't find an average without knowing how many goals were scored altogether. Think of it as sharing goals equally across all matches.

Q: What if one team scored 0 goals in a match?

Include the 0 in your calculation! Zero counts as a data point. In this problem, Match 2 had 0 goals, so we add: 4 + 0 + 5 + 6 + 2 = 17.

Q: How do I convert 17/5 to a mixed number?

Divide: 17 ÷ 5 = 3 remainder 2. So $ \frac{17}{5} = 3\frac{2}{5} $. The quotient becomes the whole number, the remainder becomes the new numerator!

Q: Can I use a decimal instead of a mixed number?

Yes! $ \frac{17}{5} = 3.4 $ goals per match. However, check what format your answer choices use. This problem gives mixed numbers, so $ 3\frac{2}{5} $ is expected.

Calculating Mean with Mixed Number Results

Below is a table describing the number of goals scored by Manchester United in each match during a season.

Calculate the average number of goals they scored per match.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a table describing the number of goals scored by Manchester United in each match during a season.

Calculate the average number of goals they scored per match.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the total number of goals scored.
Step 2: Count the total number of matches played.
Step 3: Use the formula for average to find the average number of goals scored per match.

Now, let's work through each step:

Step 1: Calculate the total number of goals scored.
The goals scored in each match are: $4$ , $0$ , $5$ , $6$ , and $2$ .
The total number of goals scored is $4 + 0 + 5 + 6 + 2 = 17$ .

Step 2: Count the total number of matches played.
There are 5 matches in total.

Step 3: Use the formula for average.
The average number of goals per match is given by:

$\text{Average} = \frac{\text{Total number of goals}}{\text{Number of matches}} = \frac{17}{5}$

Calculating the division:

$\frac{17}{5} = 3.4 = 3\frac{2}{5}$

Therefore, the average number of goals scored per match is $3\frac{2}{5}$ .

Final Answer

$3\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Mean Formula: Sum of all values divided by count
Technique: Add goals: 4 + 0 + 5 + 6 + 2 = 17, then divide by 5
Check: Convert $\frac{17}{5} = 3.4 = 3\frac{2}{5}$ matches decimal ✓

Common Mistakes

Avoid these frequent errors

Forgetting to convert improper fractions to mixed numbers
Don't leave your answer as just $\frac{17}{5}$ = wrong format! Many problems expect mixed numbers as the final answer. Always convert improper fractions like $\frac{17}{5}$ to mixed numbers: $3\frac{2}{5}$ .

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 10 $$ and $$ 12 $$ .

FAQ

Everything you need to know about this question

Why do I need to add up all the goals first?

The mean (average) requires the total sum! You can't find an average without knowing how many goals were scored altogether. Think of it as sharing goals equally across all matches.

What if one team scored 0 goals in a match?

Include the 0 in your calculation! Zero counts as a data point. In this problem, Match 2 had 0 goals, so we add: 4 + 0 + 5 + 6 + 2 = 17.

How do I convert 17/5 to a mixed number?

Divide: 17 ÷ 5 = 3 remainder 2. So $\frac{17}{5} = 3\frac{2}{5}$ . The quotient becomes the whole number, the remainder becomes the new numerator!

Can I use a decimal instead of a mixed number?

Yes! $\frac{17}{5} = 3.4$ goals per match. However, check what format your answer choices use. This problem gives mixed numbers, so $3\frac{2}{5}$ is expected.

How do I check if my mean is reasonable?

Look at your data! The goals were 4, 0, 5, 6, 2. Your mean of $3\frac{2}{5} = 3.4$ falls between the lowest (0) and highest (6), which makes sense!

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