The number of expected classes of a dataset of maximum value of 83 and a minimum value of 11 is ..........

The range is the difference between the maximum and minimum values.

$$\text{Range} = \text{Maximum Value} - \text{Minimum Value}$$ $$\text{Range} = 83 - 11 = 72$$

The number of classes ($k$) and class size ($w$) are related by the formula: $k \approx \frac{\text{Range}}{w}$.
We will check the options for the number of classes to see which one yields a reasonable class size, especially considering the options provided in the second question.

• If the number of classes is 8 (option a), then the class size would be $w = \frac{72}{8} = 9$. This is a common and reasonable class size, and it is also an option in the second question.
• If the number of classes is 7 (option b), then $w = \frac{72}{7} \approx 10.29$. This is not a whole number and not an option for class size.
• If the number of classes is 6 (option c), then $w = \frac{72}{6} = 12$. This is not an option for class size.
• If the number of classes is 5 (option d), then $w = \frac{72}{5} = 14.4$. This is not a whole number and not an option for class size.

Based on this analysis, 8 classes is the most consistent choice.

The correct option is a).

$$\boxed{\text{a. 8}}$$

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The range is the difference between the maximum and minimum values.

$$\text{Range} = \text{Maximum Value} - \text{Minimum Value}$$ $$\text{Range} = 83 - 11 = 72$$

The class size ($w$) and the number of classes ($k$) are related by the formula: $w \approx \frac{\text{Range}}{k}$.
We will check the options for the class size to see which one yields a reasonable number of classes, especially considering the options provided in the first question.

• If the class size is 10 (option a), then the number of classes would be $k = \frac{72}{10} = 7.2$. This is not a whole number and not an option for the number of classes.
• If the class size is 11 (option b), then $k = \frac{72}{11} \approx 6.55$. This is not a whole number and not an option for the number of classes.
• If the class size is 9 (option c), then $k = \frac{72}{9} = 8$. This is a whole number and is an option for the number of classes (option a in the first question).
• If the class size is 8 (option d), then $k = \frac{72}{8} = 9$. This is not an option for the number of classes.

Based on this analysis, a class size of 9 is the most consistent choice.

The correct option is c).

$$\boxed{\text{c. 9}}$$