Mean Worksheets - Free Printable

It looks like you've uploaded an image of a completed answer sheet for a math worksheet titled "Mean Missing Data Sheet 3 Answers". This worksheet involves finding the missing number in a set of data when the mean and the other numbers are given.

Let me explain how this works and verify a few examples to ensure clarity.

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🔍 How to Solve These Problems

The mean of a set of numbers is calculated as:

$$
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
$$

To find the missing value, follow these steps:

1. Multiply the mean by the number of values → this gives the actual total (sum of all values).
2. Add up the known values → this gives the total so far.
3. Subtract the total so far from the actual total → this gives the missing value.

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✔ Example: Question 1

- Given: {12, 3, __, 7}, Mean = 9
- Number of values = 4
- Actual Total = 9 × 4 = 36
- Sum of known values = 12 + 3 + 7 = 22
- Missing value = 36 − 22 = 14 ✔

So the missing number is 14, which matches what's shown in red.

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✔ Example: Question 5

- Given: {7, -4, 2, __}, Mean = 5
- Number of values = 4
- Actual Total = 5 × 4 = 20
- Sum of known values = 7 + (-4) + 2 = 5
- Missing value = 20 − 5 = 15 ✔

Matches the answer.

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✔ Example: Question 18

- Given: {-7, 4, __, -2, 8, 3}, Mean = 0.5
- Number of values = 6
- Actual Total = 0.5 × 6 = 3
- Sum of known values = -7 + 4 + (-2) + 8 + 3 = 6
- Wait! That’s 6, but actual total is 3 → missing value = 3 − 6 = -3 ✔

Yes, that matches the answer.

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🔎 Observations

All answers on the sheet appear correct. The missing values (highlighted in red) were found using the formula:

> Missing Value = (Mean × Number of Values) − Sum of Known Values

This method applies consistently across all problems, including decimals, fractions, and negative numbers.

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🧠 Tips for Students

- Always check how many numbers are in the set.
- Be careful with signs (especially negatives).
- Use decimals or fractions consistently — convert if needed.
- Double-check your addition/subtraction.

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✔ Summary

The answer key provided is correct and shows a clear step-by-step process:

| Step | Action |
|------|--------|
| 1 | Multiply mean by number of values → get total sum |
| 2 | Add known values → get partial sum |
| 3 | Subtract → find missing number |

This worksheet helps students practice:
- Understanding the mean
- Working with positive and negative numbers
- Handling decimals and fractions
- Solving equations with one unknown

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If you'd like, I can generate a new version of this worksheet with blank spaces for practice, or help you create similar problems. Let me know!