6 numbers from 0 to 9 that have a median of 4, a mean of 4 and a mode of 3

To determine 6 numbers between 0 and 9 that meet the following criteria:

1. **Median of 4**: The middle two numbers (when sorted) must average to 4, as there are 6 numbers.
2. **Mean of 4**: The sum of the numbers must be \( 6 \times 4 = 24 \).
3. **Mode of 3**: The number 3 must appear more often than any other number.

### Step-by-step solution:

#### 1. Median of 4
For the median to be 4, the middle two numbers (when sorted) must be either:
- Both 4 (\(4+4)/2 = 4\), or
- Numbers that average to 4, such as 3 and 5.

#### 2. Mode of 3
To ensure the mode is 3, 3 must appear at least twice, preferably more.

#### 3. Mean of 4
The total of the 6 numbers must be \( 24 \). 

#### Possible solution:
Consider:
\[
\{3, 3, 4, 4, 5, 5\}
\]

- **Median**: The two middle numbers are 4 and 4. Their average is 4.
- **Mean**: \( \frac{3+3+4+4+5+5}{6} = \frac{24}{6} = 4 \).
- **Mode**: The number 3 appears most often (twice).

Thus, \(\{3, 3, 4, 4, 5, 5\}\) satisfies all the criteria.

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Would you like more details or additional variations? 

### Related questions:
1. Can there be another set of numbers with the same constraints?
2. How does the mode influence the uniqueness of the set?
3. What happens if the range of numbers is restricted further?
4. How can these principles apply to data analysis problems?
5. Is there a way to find sets of numbers algorithmically for similar constraints?

### Tip:
Always verify each condition (mean, median, mode) step by step to ensure accuracy when constructing such datasets.

6 numbers from 0 to 9 that have a median of 4, a mean of 4, and a mode of 3.

Discover how to determine a set of 6 numbers between 0 and 9 with a mean of 4, a median of 4, and a mode of 3. Includes step-by-step calculations and verification of statistical properties, ideal for Grades 6-8 students.

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