Let's go through the data in the stem-and-leaf plot and fill in the missing information.

Stem-and-Leaf Plot Values:

• Stem 2: 23, 23, 28, 29
• Stem 3: 30, 34, 37
• Stem 4: 45, 45, 45
• Stem 5: 57

Given Information:

1. Highest value: 57
2. Smallest value: 23
3. Range: $57 - 23 = 34$
4. Mode: 45 (it appears three times)
5. Median: 34

Let's find the mean:

Step-by-step Solution for the Mean:

Add all the values together: $23 + 23 + 28 + 29 + 30 + 34 + 37 + 45 + 45 + 45 + 57 = 396$

Now, divide by the number of values (11): $\text{Mean} = \frac{396}{11} = 36$

Summary

• Mean: 36

If you have any questions or want further explanations, let me know!

Follow-up Questions:

1. What is the impact of having a mode that appears multiple times in a data set?
2. Can you find the quartiles for this stem-and-leaf plot?
3. What would be the variance and standard deviation of these values?
4. How would the mean change if we added another value, say 60, to the set?
5. What is the difference between mean, median, and mode in interpreting data?

Tip: The mean gives a central value for a data set, but it is sensitive to extreme values (outliers).