Let's calculate the mean, median, and mode for the given data set:

Data Set: 96.9, 96.9, 71.4, 82.6, 96.9, 76, 77, 67, 65.4, 59.9

1. Mean: $\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{96.9 + 96.9 + 71.4 + 82.6 + 96.9 + 76 + 77 + 67 + 65.4 + 59.9}{10} = \frac{ 812.9}{10} = 81.29$

2. Median: First, arrange the data in ascending order: 59.9, 65.4, 67, 71.4, 76, 77, 82.6, 96.9, 96.9, 96.9. Since there are 10 values (even), the median is the average of the 5th and 6th values: $\text{Median} = \frac{76 + 77}{2} = \frac{153}{2} = 76.5$

3. Mode: The mode is the value that appears most frequently, which is 96.9 (it appears 3 times).

Summary:

• Mean: 81.29
• Median: 76.50
• Mode: 96.90

Would you like more details or have any questions? Here are some follow-up questions you might consider:

1. How do you calculate the range of this data set?
2. What is the significance of the mode in this context?
3. How would the mean change if we added a new data point?
4. What other measures of central tendency might be relevant?
5. Can you explain the differences between mean, median, and mode?

Tip: Always check for outliers, as they can significantly affect the mean!