Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median $$ =78 $$, mean $$ =79 $$, low score $$ =65 $$, high score $$ =87 $$ The distribution is right-skewed

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1. **Identify the given data:**

- Median: $$78$$
   - Mean: $$79$$
   - Low score (minimum): $$65$$
   - High score (maximum): $$87$$

2. **Determine the shape of the distribution:**

- Since the mean $$ (79) $$ is slightly greater than the median $$ (78) $$, this implies that the distribution has a longer tail to the right. In other words, a few higher scores are pulling the mean upward.
   - Therefore, the distribution is **right-skewed**.

3. **Assess the variation of the distribution:**

- The range of the data can be calculated as:
     
     $$
     \text{Range} = \text{High score} - \text{Low score} = 87 - 65 = 22
     $$
     
   - This range of $$22$$ indicates the spread of the scores.
     
     While additional measures like the standard deviation would give more insight into the variation, the range provides a basic overview of how widely the scores extend.

4. **Final description:**

The exam scores are distributed over a range of $$22$$ points, from $$65$$ to $$87$$. The mean is higher than the median, indicating that the distribution is right-skewed (positively skewed) due to the presence of a few higher scores.

The exam scores are spread from 65 to 87, with a mean slightly higher than the median, indicating a right-skewed distribution.

Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median \( =78 \), mean \( =79 \), low score \( =65 \), high score \( =87 \) The distribution is right-skewed

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