MEGA Elementary Education Multi-Content Practice Test

From which graphical representation can the median of a data set be most efficiently determined?

1. Box plot

2. Frequency diagram

3. Stem-and-leaf plot

4. Histogram

The correct answer is: Box plot

The median of a data set can be most efficiently determined from a box plot because it is specifically designed to present summary statistics visually. The box plot displays the five-number summary of a data set, which includes the minimum, first quartile, median, third quartile, and maximum. The median is represented by a line within the box, making it very easy to identify at a glance. In contrast, while other graphical representations like frequency diagrams, stem-and-leaf plots, and histograms can provide insights into the distribution of the data, they require more steps to locate the median. For example, in a histogram, you would need to interpret the data intervals and calculate cumulative frequencies to find the median, which is less direct than the straightforward visual representation in a box plot. Therefore, the box plot stands out as the most efficient tool for quickly determining the median of a data set.