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Comparing Two Populations: Center, Variability, and Informal Inference

Show all work for MAD and IQR computations. When writing inference statements, include center values, variability measures, and hedging language.

Grade 7·21 problems·~45 min·Common Core Math - Grade 7·standard·7-sp-b-4

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A random sample of word lengths from two science textbooks produced these results: 4th-grade — median = 5 letters, IQR = 2 letters; 7th-grade — median = 7 letters, IQR = 3 letters. Which statement best compares the two samples?

Words in the 7th-grade text are exactly 2 letters longer than words in the 4th-grade text.

Words in the 7th-grade text tend to be about 2 letters longer than words in the 4th-grade text; the 7th-grade text also has slightly more variability in word length (IQR = 3 vs. 2).

The 7th-grade text has a higher median, so all of its words are longer than 4th-grade words.

The two samples cannot be compared because the IQR values are different.