Ohio Assessments for Educators (OAE) Mathematics Practice Exam

In a box and whiskers plot, what do the end points of the box represent?

1. First and third quartiles

2. Minimum and maximum values

3. Median and mode

4. Mean and standard deviation

The correct answer is: First and third quartiles

In a box and whiskers plot, the endpoints of the box specifically represent the first quartile (Q1) and the third quartile (Q3). The first quartile, Q1, is the value at which 25% of the data points fall below it, while the third quartile, Q3, is the value at which 75% of the data points fall below it. The box itself therefore provides a visual representation of the interquartile range, which indicates the spread of the middle 50% of the data. The whiskers that extend from the box typically represent the minimum and maximum values of the dataset, but the endpoints of the box are distinct in that they specifically mark the quartiles, allowing viewers to quickly grasp the distribution of the data in terms of its central tendency and variability. This understanding of the quartiles is fundamental in statistics, as it allows for better interpretation of data sets in various contexts. The other choices do not accurately reflect what the endpoints of the box denote in a box and whiskers plot. For example, the median would not be represented by the box's endpoints but would typically be marked by a line within the box instead.