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

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.