Questions: Use a stem-and-leaf plot to display the data, which represent the scores of a biology class on a midterm exam. Describe any patterns. 75, 85, 90, 80, 87, 67, 82, 88, 95, 91, 77, 80, 85, 92, 94, 68, 75, 91, 93, 87, 76, 91, 85, 99 Determine the leaves in the stem-and-leaf plot below. Key: 3 3=33 Exam Scores 6 7 8 9

Solution Steps

To create a stem-and-leaf plot, we first separate each score into a stem (the leading digit(s)) and a leaf (the trailing digit). For this data set, the tens digit will be the stem, and the units digit will be the leaf. We then organize the data by stems and list the leaves in ascending order for each stem. Finally, we can describe any patterns observed in the distribution of scores.

To create a stem-and-leaf plot, we first separate each score into a stem and a leaf. The stem is the tens digit, and the leaf is the units digit. For example, the score 75 has a stem of 7 and a leaf of 5.

Next, we group the leaves by their corresponding stems and sort them in ascending order. The organized data is as follows:

• Stem 6: Leaves \(7, 8\)
• Stem 7: Leaves \(5, 5, 6, 7\)
• Stem 8: Leaves \(0, 0, 2, 5, 5, 5, 7, 7, 8\)
• Stem 9: Leaves \(0, 1, 1, 1, 2, 3, 4, 5, 9\)

Using the organized data, we construct the stem-and-leaf plot: \[ \begin{align_} 6 & \mid 7 \, 8 \\ 7 & \mid 5 \, 5 \, 6 \, 7 \\ 8 & \mid 0 \, 0 \, 2 \, 5 \, 5 \, 5 \, 7 \, 7 \, 8 \\ 9 & \mid 0 \, 1 \, 1 \, 1 \, 2 \, 3 \, 4 \, 5 \, 9 \\ \end{align_} \]

From the stem-and-leaf plot, we can observe the following patterns:

• The scores are concentrated in the 80s and 90s, indicating a higher performance in the class.
• There are fewer scores in the 60s, suggesting that lower scores are less common.
• The distribution is slightly skewed towards the higher end, with more scores in the 90s.

Final Answer