To analyze the histogram data provided, let's start by determining whether the distribution is skewed left or right, identifying the mode, and calculating the range.
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Skewness:
- The frequencies of the grades are as follows:
- 50–64: 2
- 65–74: 4
- 75-80: 1
- 81-85: 5
- 85-94: 8
- 95-100: 6
- The highest frequencies occur in the upper grades (85-94) and lower frequencies in the lower grade ranges (50-64 and 75-80). This indicates that there are more high grades than low grades, suggesting the data is skewed to the left (or negatively skewed).
- The frequencies of the grades are as follows:
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Mode:
- The mode is the range with the highest frequency. Here, the range with the highest frequency is 85-94, which has a frequency of 8.
- Therefore, the mode is in the range 85-94.
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Range:
- The range of the data is calculated by subtracting the lowest grade from the highest grade.
- The lowest grade represented is 50 (from the range 50-64) and the highest grade represented is 100 (from the range 95-100).
- Thus, the range is \(100 - 50 = 50\).
In conclusion:
- The data are skewed left.
- The mode is 85-94.
- The range is 50.