Question

Kono gathers the heights of a random sample of sixth graders and seventh graders and displays the data in box plots. What can he say about the two data sets?

The median of the grade sample is greater than the median of the grade sample.

The grade sample has greater variability.



Convince Me!

How can you visually compare data from two samples that are displayed in box plots?

Two box plots. 6th grade students minimum is 56, 1st quartile is 58, median is 62, 3rd quartile is 64, maximum is 69. 7th grade student's minimum is 53, 1st quartile is 58, median is 63, 3rd quartile is 68, maximum is 74.

Answer 1

Yes — both of the given statements are true. Use the numbers from the box plots to justify them.

Compare medians:
- 6th grade median = 62
- 7th grade median = 63
So the 7th-grade median is larger than the 6th-grade median.

Compare variability (middle 50% and overall):
- 6th grade IQR = Q3 − Q1 = 64 − 58 = 6
- 7th grade IQR = 68 − 58 = 10 → 7th grade has a larger IQR (more spread in the middle 50%).
- 6th grade range = 69 − 56 = 13
- 7th grade range = 74 − 53 = 21 → 7th grade has a larger overall range.

How to visually compare two box plots (what to look for)
- Median line: compares centers (which sample is taller on average/typical).
- Box length (IQR): compares variability of the middle 50% (longer box = more variability).
- Whisker lengths / total range: compares overall spread and presence of extreme values.
- Position of median inside the box and relative whisker lengths: indicates skewness.
- Outliers (if shown): indicate extreme observations.

Using those visual cues and the numerical values above, you can conclude: 7th graders tend to be slightly taller (median 63 vs 62) and show greater variability (IQR 10 vs 6, range 21 vs 13).