To analyze the data represented in the stem-and-leaf display, let's break down the process step by step:

Stem-and-Leaf Breakdown:

• Stem represents the tens place of the scores.
• Leaf represents the ones place of the scores.

So, the data is:

• 40s: 47
• 50s: 51, 53, 54
• 60s: 63, 64, 64, 65, 65, 66, 66
• 70s: 70, 71, 72, 72, 73, 73, 74, 74, 74, 74, 79
• 80s: 80, 81, 83, 84, 85, 86, 86
• 90s: 90, 91, 92, 92, 94

Now, let's calculate the mean, median, and mode.

---

1. Mean (Average):

The mean is the sum of all scores divided by the total number of scores.

• Sum of the scores = 47 + 51 + 53 + 54 + 63 + 64 + 64 + 65 + 65 + 66 + 66 + 70 + 71 + 72 + 72 + 73 + 73 + 74 + 74 + 74 + 74 + 79 + 80 + 81 + 83 + 84 + 85 + 86 + 86 + 90 + 91 + 92 + 92 + 94 = 2397
• Total number of scores = 34 (as per the problem).

Mean = $\frac{2397}{34} \approx 70.65$

---

2. Median:

The median is the middle value when the data is arranged in ascending order. Since there are 34 data points (an even number), the median is the average of the 17th and 18th scores.

• The 17th and 18th scores (in order) are 73 and 73.

Median = $\frac{73 + 73}{2} = 73$

---

3. Mode:

The mode is the score that appears most frequently in the data.

From the stem-and-leaf display, we can see that the most frequent score is 74, which appears 4 times.

Mode = 74

---

Summary:

• Mean = 70.65
• Median = 73
• Mode = 74

Would you like more details on how to calculate any of these values or have any questions about the steps?

---

Additional Questions:

1. What are the advantages and disadvantages of using the mean, median, and mode to describe a data set?
2. How would the median change if we had an odd number of data points instead of an even number?
3. How does the presence of outliers affect the mean and median?
4. What is the impact of adding a new data point that is much higher than all existing points on the mean and median?
5. How could you use the stem-and-leaf display to quickly identify the range of the scores?

Tip: When calculating the median for an even number of values, always average the two middle values to get the correct result.