The image shows a stem-and-leaf plot, followed by a series of questions regarding the data. Let’s first extract the values from the plot:

• Stem 9: 94, 94, 97, 99
• Stem 10: 106, 107, 109
• Stem 11: 113, 113
• Stem 12: 122, 123

Thus, the data set is: $94, 94, 97, 99, 106, 107, 109, 113, 113, 122, 123$

Now, let's solve the questions:

1. Highest value: The highest value in the data set is 123.
2. Smallest value: The smallest value is 94.
3. Range: The range is calculated as the difference between the highest and smallest value: $\text{Range} = 123 - 94 = 29$
4. Mode: The mode is the most frequently occurring value. In this case, 94 and 113 both occur twice, so the mode is 94 and 113.
5. Median: The median is the middle value of the ordered data set. Since there are 11 values, the 6th value is the median: $\text{Median} = 107$
6. Mean: The mean is the average of the values. Sum all the values and divide by the total number of values (11): $\text{Mean} = \frac{94 + 94 + 97 + 99 + 106 + 107 + 109 + 113 + 113 + 122 + 123}{11} = \frac{1177}{11} \approx 107$

Summary:

• Highest value = 123
• Smallest value = 94
• Range = 29
• Mode = 94, 113
• Median = 107
• Mean = 107

Would you like further details on any of the calculations or concepts?

Here are some related questions:

1. What happens to the mode if another 99 is added to the data?
2. How is the range affected by adding a new value, say 125, to the set?
3. What would the median be if the number of data points were even instead of odd?
4. Can the mode be used to determine the "center" of the data effectively?
5. How does the mean change if an outlier, like 150, is introduced?

Tip: The median is often more representative of the "typical" value in a dataset when there are outliers or skewed data.