Question

when the data is quantitative, line graphs, histograms, stem-and-leaf plots, or box-and-whisker plots are more appropriate choices.

• each of these types of data displays is used for different purposes.
• line graphs show how data changes over time.
• histograms, stem-and-leaf plots, and box-and-whisker plots show the frequency of data and how it is distributed.

stem-and-leaf plots and box-and-whisker plots can give you a good picture of what the data is doing. the stem-and-leaf plot provides detail and is extremely easy to construct, while the box-and-whisker plot clearly shows the data’s median, quartiles, and outliers.
suppose that a teacher gives a math test and the scores are as follows: 36, 54, 55, 55, 56, 56, 61, 62, 64, 64, 68, 70, 73, 74, 76, 76, 77, 77, 77, 77, 78, 80, 83, 85, 85, 85, 89, 91, 91, 92, 94, and 97.

• use the list of test scores to finish constructing the stem-and-leaf plot to the right. remember that in this type of plot, the largest place value is listed to left and makes up the stem, while the smaller place value is shown to the right and is the leaf.

the same test scores are shown on the box-and-whisker plot below, right.

• use your prior knowledge to label the first quartile, median, and third quartile on the plot.
• why might you choose to use a box-and-whisker plot over a stem-and-leaf plot? write your answer in the box below.

stem | leaf
9 | 1 1 2 4 7
8 | 0 3 5 5 5 9
7 | 0 3 4 6 6 7 7 7 7 8
6 | 1 2 4 4 8
5 | 4 5 5 6 6
4 |
3 | 6

box-and-whisker plot with axis: 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100

Explanation:

For the question "Why might you choose to use a box - and - whisker plot over a stem - and - leaf plot?"

A box - and - whisker plot is better for quickly identifying the overall spread (range), the median, quartiles, and outliers of the data. It gives a concise summary of the data's central tendency and variability. In contrast, a stem - and - leaf plot shows more detailed individual data points but can be more cluttered when there are many data points. So, if we want a quick overview of the data's distribution characteristics like the middle 50% of the data (interquartile range), median, and presence of outliers, a box - and - whisker plot is more suitable. Also, it is easier to compare multiple data sets using box - and - whisker plots as the visual representation of the five - number summary (minimum, first quartile, median, third quartile, maximum) is straightforward.

Answer:

A box - and - whisker plot can be chosen over a stem - and - leaf plot because it provides a concise visual summary of the data's spread (including quartiles, median, range, and outliers), making it easier to quickly analyze the central tendency and variability of the data. It is also more effective for comparing multiple data sets at a glance, while a stem - and - leaf plot focuses more on showing individual data points in detail.