The table below shows the scores of a group of students on a 10-point quiz.

Test ScoreFrequency

3

1

4

3

5

1

6

4

7

1

8

1

9

5

10

2

The mean score on this test is:

The median score on this test is:

To find the mean and median scores from the given data, we first summarize the scores and their frequencies:

| Test Score | Frequency |
|------------|-----------|
| 3          | 1         |
| 4          | 3         |
| 5          | 1         |
| 6          | 4         |
| 7          | 1         |
| 8          | 1         |
| 9          | 5         |
| 10         | 2         |

### Mean Calculation
1. **Calculate the total score:**
   \[
   \text{Total Score} = (3 \times 1) + (4 \times 3) + (5 \times 1) + (6 \times 4) + (7 \times 1) + (8 \times 1) + (9 \times 5) + (10 \times 2)
   \]
   \[
   = 3 + 12 + 5 + 24 + 7 + 8 + 45 + 20 = 124
   \]

2. **Calculate the total frequency:**
   \[
   \text{Total Frequency} = 1 + 3 + 1 + 4 + 1 + 1 + 5 + 2 = 18
   \]

3. **Calculate the mean:**
   \[
   \text{Mean} = \frac{\text{Total Score}}{\text{Total Frequency}} = \frac{124}{18} \approx 6.89
   \]

### Median Calculation
To find the median, we need to determine the middle score when all scores are listed in order:

- The cumulative frequency helps us find the median position:
  - Score 3: 1 (1 total)
  - Score 4: 3 (4 total)
  - Score 5: 1 (5 total)
  - Score 6: 4 (9 total)
  - Score 7: 1 (10 total)
  - Score 8: 1 (11 total)
  - Score 9: 5 (16 total)
  - Score 10: 2 (18 total)

The median is at the \(\frac{n + 1}{2}\)th position, where \(n\) is the total frequency. Thus, the median is at position \(\frac{18 + 1}{2} = 9.5\), which falls between the 9th and 10th scores.

From the cumulative frequency, the 9th score is 6 and the 10th score is 7. Therefore, the median is:
\[
\text{Median} = \frac{6 + 7}{2} = 6.5
\]

### Summary
- **Mean Score:** Approximately 6.89
- **Median Score:** 6.5

Would you like more details or have any questions? Here are some related questions:

1. How do you calculate the mode from this data?
2. What are the implications of the mean and median being different?
3. How would you visualize this data using a histogram?
4. What happens to the mean if an additional student scores a 10?
5. Can you explain the concept of cumulative frequency? 

**Tip:** Always check if the mean or median is more appropriate for your data analysis based on its distribution.

The table below shows the scores of a group of students on a 10-point quiz. What is the mean and median score on this test?

Explore how to calculate the mean and median scores from a group of student quiz scores. This solution illustrates the step-by-step process, revealing a mean score of approximately 6.89 and a median score of 6.5. Ideal for Grades 6-8.

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