Questions: Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median = 67, mean = 76, low score = 64, high score = 84

Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution.
median = 67, mean = 76, low score = 64, high score = 84

Transcript text: Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median $=67$, mean $=76$, low score $=64$, high score $=84$

Solution

Solution Steps

Step 1: Calculate the Range

The range of the exam scores is calculated as follows:

\[ \text{Range} = \text{High Score} - \text{Low Score} = 84 - 64 = 20 \]

Step 2: Determine the Shape of the Distribution

To analyze the shape of the distribution, we compare the mean and median:

Given $ \text{Mean} = 76 $ and $ \text{Median} = 67 $.
Since $ \text{Mean} > \text{Median} $, the distribution is classified as right-skewed.

Step 3: Assess the Variation

The variation of the distribution is evaluated based on the range:

The calculated range is $ 20 $.
Since $ 20 $ is greater than $ 10 $, we conclude that the distribution has low variation.

Final Answer

The distribution is right-skewed and has low variation. Thus, we can summarize the findings as follows:

\[ \boxed{\text{Distribution: right-skewed, Variation: low}} \]

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