Question

A local recreation center offers a drop-in exercise class in the morning and in the evening. The attendance data for each class over the first month is shown in the box plots at the right. What can you infer about the class attendance?

Answer 1

I don’t see the box plots you mentioned — could you upload the image or describe the five-number summaries (minimum, Q1, median, Q3, maximum) for each class?

Meanwhile, here’s how to read and compare the two box plots and the kinds of conclusions you can draw:

What each part tells you
- Median (line in the box): the typical attendance (middle of the month).
- Box (Q1 to Q3, the IQR): where the middle 50% of attendance lies — smaller box = more consistent attendance.
- Whiskers (to min and max or to last non-outlier): overall spread; long whiskers = large variability or occasional very low/high days.
- Outliers (points beyond whiskers): unusually low/high attendance days.
- Skew: if the median is closer to one side of the box or one whisker is much longer, the distribution is skewed.

Types of inferences you can make (examples)
- If one class has a higher median than the other: that class usually has more people.
- If one class has a smaller IQR: its attendance is more consistent from day to day.
- If one class has much longer whiskers or more outliers: its attendance is more variable and has occasional extremes.
- If the box/whiskers are shifted right: attendance tends to be higher overall.
- If medians are similar but one has a much larger spread: both classes have similar typical attendance, but one is less predictable.

Example statements you could write once you have the plots
- “The evening class has a higher median and higher maximum, so it generally attracts more people than the morning class.”
- “The morning class’s box is much narrower, indicating more consistent attendance, while the evening class is more variable with several high-attendance outliers.”
- “Both classes have similar medians, but the evening class shows a right skew (long upper whisker), suggesting occasional very busy days.”

Send the image or the five-number summaries and I’ll give a precise comparison and suggested phrasing.