To answer these questions, let’s analyze the information given:

(a) Which class's scores have the most variability?

The variability in scores can be inferred from the range since it measures the spread between the highest and lowest scores in each class. The class with the largest range has the most variability.

• Class A: Range = 38
• Class B: Range = 31
• Class C: Range = 34
• Class D: Range = 33

Answer for (a): Class A has the most variability because it has the largest range of 38.

(b) Which class has the lowest scores on average?

The average score of each class is represented by the mean. The class with the lowest mean has the lowest scores on average.

• Class A: Mean = 109
• Class B: Mean = 116
• Class C: Mean = 113
• Class D: Mean = 108

Answer for (b): Class D has the lowest scores on average, with a mean score of 108.

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Here are five additional questions based on this problem:

1. What other measures of variability, besides the range, could we use to analyze the spread of scores?
2. How would the standard deviation of each class's scores compare if calculated?
3. If the range in Class B were increased, how would that affect its variability relative to Class A?
4. How would the results change if the mean scores of each class were closer together?
5. What additional data would help us analyze the scores more comprehensively?

Tip: Remember, range is a basic measure of spread, but standard deviation provides a more accurate measure of how scores vary around the mean.