Stemplots (Stem-and-Leaf Plots): Videos & Practice Problems

Histograms are effective for visualizing quantitative data, but they may not provide specific values, which can limit their usefulness for certain analyses. An alternative method for displaying numerical data is the stemplot, which not only shows trends but also retains the specific values from the dataset. Creating a stemplot involves a few straightforward steps, starting with organizing the data.

The first step is to arrange the data in increasing order. This organization simplifies the subsequent steps and ensures accuracy in representation. Once the data is sorted, the next step is to draw a vertical line, which serves as the foundation for the stemplot.

In a stemplot, data points are divided into stems and leaves. The leaf is defined as the rightmost digit of each data point, while the stem consists of the remaining digits to the left. For example, in the number 20, the stem is 2 and the leaf is 0. Similarly, for 105, the stem is 10 and the leaf is 5. This division is crucial for accurately representing the data.

After identifying the stems, they should be listed in ascending order on the left side of the vertical line, ensuring that each stem is only listed once, regardless of how many data points share that stem. For instance, if the dataset includes the numbers 20, 31, 33, and 35, the stems would be listed as 2, 3, and 4, with the leaves corresponding to each stem placed in the rightmost column.

Each leaf represents a data point and is placed in the same row as its corresponding stem. It is important to note that leaves are listed without commas. For example, if the stem is 4 and the leaves are 0, 2, 5, and 5, they would be written as 0 2 5 5 in the same row as the stem 4.

Once all leaves are added, the stemplot is complete, providing a clear visual representation of the dataset that highlights both the distribution and specific values. This method is particularly useful for identifying trends and patterns within the data. Students can further enhance their understanding by practicing with examples and exercises related to stemplots.

In this practice on stemplots, we analyze the test scores of two classes to extract meaningful insights. A stemplot visually represents data, where the left side of the vertical line shows the tens digits (stems) and the right side displays the ones digits (leaves). For instance, a score of 67 is represented as 6 | 7, where 6 is the stem and 7 is the leaf.

To determine the highest and lowest scores in each class, we first identify the highest scores by examining the tens column. For Class A, the highest score is found in the nineties, specifically 98, while Class B's highest score is 96. Conversely, the lowest scores are identified by looking at the lowest tens row. Class A's lowest score is 67, and Class B's is 63.

Next, we assess the number of students scoring in the seventies, which corresponds to receiving a grade of C. By counting the leaves in the seventies row, we find that Class A has six students scoring in this range, while Class B has eight students, indicating that Class B has more students receiving a C.

Finally, we compare the overall distributions of test scores between the two classes. Notably, both classes have the highest frequency of scores in the eighties, indicating this is the most popular range. However, Class B appears to perform worse overall, as evidenced by its lower minimum score (63 vs. 67) and maximum score (96 vs. 98). Additionally, Class B has more students scoring in the lower ranges (sixties and seventies), while Class A has a longer row of nineties, suggesting better performance in higher scores.

In summary, analyzing stemplots allows us to draw conclusions about the performance of different groups by comparing their highest and lowest scores, the distribution of grades, and the overall trends in their test scores.