Questions: Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median = 75, mean = 77, low score = 63, high score = 87 The distribution is square and has square variation.

Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median = 75, mean = 77, low score = 63, high score = 87 The distribution is square and has square variation.
Transcript text: Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. \[ \text { median }=75, \text { mean }=77, \text { low score }=63, \text { high score }=87 \] The distribution is $\square$ and has $\square$ variation.
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Solution

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Solution Steps

To describe the shape and variation of the distribution, we can use the given statistical measures. The mean is slightly higher than the median, which suggests a slight right skew in the distribution. The range, calculated as the difference between the high score and the low score, will give us an idea of the variation.

Step 1: Determine the Shape of the Distribution

Given that the mean \( \mu = 77 \) is greater than the median \( \text{median} = 75 \), we can conclude that the distribution is right skewed. This indicates that there are more lower scores pulling the median down compared to the mean.

Step 2: Calculate the Variation

The variation of the distribution can be calculated using the range, which is given by: \[ \text{Range} = \text{high score} - \text{low score} = 87 - 63 = 24 \] Thus, the variation of the distribution is \( 24 \).

Final Answer

The distribution is right skewed and has a variation of \( 24 \). Therefore, the final answer is: \[ \boxed{\text{right skewed, variation = 24}} \]

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