A middle school mathematics teacher poses the following question to her class.…

The choice of a statistical graph depends on the nature of the data being shown. A bar graph is used to compare separate, named categories against each other. A line graph is used to track how a single continuously measured quantity changes over time. A pie chart shows how one whole splits into proportional parts. A histogram displays the frequency distribution of a continuous variable by dividing its full range into class intervals and showing how many observations fall into each interval.

In this question, both parts ask the class to divide a continuous variable's range into intervals and then count how many observations fall in each interval — not to compare a short list of categories, not to plot one continuously measured quantity's trend, and not to split one total into proportional shares. For (a), the continuous variable is height: participants' heights are grouped into height-intervals, and the frequency in each interval is the number of participants whose height falls there. For (b), the continuous variable is time across the day: the 9:00 am-9:00 pm span is divided into hourly intervals, and the frequency in each interval is the number of passengers who boarded during that hour. Both scenarios share exactly the histogram structure — a continuous range split into class intervals with a frequency count attached to each — so by pairing these two different-looking contexts, the teacher is checking whether students can recognise when a histogram, rather than some other graph, is the right choice.

• A bar-graph-versus-line-graph contrast fits when the task is comparing a handful of separate named categories, which is not what either example asks for here.

• A pie chart fits when the task is showing proportional shares of one single total, not spreading many measurements across a range.

• A line graph fits when a single continuously measured quantity (such as temperature or altitude) is plotted against time to show its trend — not when the task is to count how many discrete events (like passengers boarding) fall inside each interval of time, which calls for a frequency-based histogram instead.

Since both examples call for organising many continuous values into class intervals and reading off their frequencies, the teacher's intention is to teach the use of histograms for data representation.