Let's solve the problem step by step based on the data provided:

Data:

92, 85, 97, 87, 96, 68, 92, 88, 82, 75, 72

1. Mean (Average):

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

$\text{Sum of all values} = 92 + 85 + 97 + 87 + 96 + 68 + 92 + 88 + 82 + 75 + 72 = 944$

$\text{Number of values} = 11$

$\text{Mean} = \frac{944}{11} \approx 85.8$

2. Mode:

The mode is the number that occurs most frequently. From the data:

• 92 appears twice.
• All other numbers appear once.

$\text{Mode} = 92$

3. Range:

$\text{Range} = \text{Maximum value} - \text{Minimum value}$

$\text{Maximum value} = 97, \, \text{Minimum value} = 68$

$\text{Range} = 97 - 68 = 29$

4. Median:

The median is the middle value when the numbers are arranged in order. If there are an odd number of values, it's the middle one.

Arrange the data in ascending order:

68, 72, 75, 82, 85, 87, 88, 92, 92, 96, 97

There are 11 numbers, so the middle value is the 6th number: $\text{Median} = 87$

Final Answers:

• Mean = 85.8
• Mode = 92
• Range = 29
• Median = 87

Do you want further explanation or have additional questions?
Here are 5 related questions to expand understanding:

1. What if there were multiple modes in the dataset?
2. How is the range affected if one extreme value is removed?
3. Can you explain how the mean might differ from the median in a skewed dataset?
4. What does the mode tell us about the data distribution?
5. How would the calculations change if we added a new number, such as 100?

Tip: Always double-check your calculations for large datasets by re-summing values!