Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does a box plot visually summarize about a data set?

1. The central tendency and overall variability

2. The frequency of each data point

3. The exact values of all individual data points

4. Only the maximum and minimum values

The correct answer is: The central tendency and overall variability

A box plot is a powerful visual representation that summarizes several key aspects of a data set. Primarily, it conveys information about the central tendency and overall variability of the data. The box plot includes the median, which indicates the central tendency, and it shows the interquartile range (IQR), which reflects the overall variability. This visual tool effectively captures how the data distributes around the median and provides insights into the spread, including potential outliers. While frequency of data points is essential for understanding distributions, a box plot does not directly depict how often each data value occurs. Similarly, though the exact values of individual data points offer a granular view of a dataset, a box plot does not specifically include these values; rather, it summarizes them through quartiles. Lastly, noting only the maximum and minimum values provides a limited view and does not encapsulate the full distribution and variability of the data set represented in a box plot. Thus, the primary focus of a box plot is indeed on summarizing the central tendency and variability, making it a valuable tool for quickly assessing these characteristics in a data set.