Select the correct answer.
The ages of the people who attend a weekly yoga class at the local yoga studio are shown in the table below.
Which data display(s) can be used to find the median for the ages of the yoga students?
I. box plot
II. dot plot
III. histogram
A. II and III
B. I, II, and III
C. I and II
D. I only
Answer (1)
Box plots display the median directly.
Dot plots allow easy sorting to find the median.
Histograms group data, making it difficult to find the exact median.
Therefore, box plots and dot plots can be used to find the median. C
Explanation
Understand the problem We are given a set of ages of yoga students and asked to determine which data displays can be used to find the median age. The possible data displays are box plots, dot plots, and histograms.
Box Plot A box plot displays the median directly as a line within the box. Therefore, a box plot can be used to find the median.
Dot Plot A dot plot shows each data point, allowing us to easily sort the data and find the middle value (median). Therefore, a dot plot can be used to find the median.
Histogram A histogram groups data into bins. While it shows the frequency distribution, it does not directly display the individual data points. Therefore, it is difficult to find the exact median from a histogram without the original data.
Conclusion Since box plots and dot plots can be used to find the median, the correct answer is C.
Examples
Understanding data distributions is crucial in many real-world scenarios. For instance, in healthcare, analyzing the distribution of patient ages can help hospitals allocate resources effectively. Knowing the median age, along with other measures like quartiles (which are easily obtained from a box plot), allows for better planning and tailored healthcare services. Similarly, in education, understanding the distribution of student test scores helps teachers identify areas where students may need additional support. A box plot or dot plot can quickly reveal the median score and the spread of the data, providing valuable insights for instructional adjustments.
