Measurement and Data>Comparing Two Populations Using Data and Random Samples(TEKS.Math.7.12.C)
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Texas 7th Grade Math › Measurement and Data>Comparing Two Populations Using Data and Random Samples(TEKS.Math.7.12.C)
Two random samples were taken to compare daily reading time. Population A (n=30): median 35 minutes, IQR 12 minutes. Population B (n=28): median 42 minutes, IQR 20 minutes. Which inference is most reasonable?
Every student in Population B reads more than every student in Population A because B's median is higher.
The populations read exactly the same amount because the IQRs are not equal.
Based on these samples, Population B tends to read more on average, but reading times are more variable.
Population A reads more because a smaller IQR means higher reading time.
Explanation
This is an informal, sample-based comparison. The center (median) is higher for Population B (42 vs 35), suggesting B tends to read more, but B also has a larger spread (IQR 20 vs 12), so results are more variable and not true for every individual.
Two random samples of quiz scores were collected. Class X (n=25): mean 78, MAD 6. Class Y (n=24): mean 82, MAD 11. Which inference is most reasonable?
Based on these samples, Class Y tends to score higher on average, but results are more variable.
Class Y is definitely better for every student because its mean is higher.
Because Class Y's MAD is larger, the means cannot be compared at all.
Class X must have higher scores overall because its MAD is smaller.
Explanation
This is an informal inference from samples. The center (mean) is higher for Class Y (82 vs 78), suggesting higher typical scores, but the spread (MAD) is also larger (11 vs 6), indicating more variability and not a guarantee for every student.
Heights of seedlings from two garden areas were sampled. Sun area (n=20): median 14 cm, IQR 4 cm. Shade area (n=20): median 12 cm, IQR 2 cm. Which inference is most reasonable?
Shade seedlings are shorter for every plant because their IQR is smaller.
The two areas produce identical heights because the medians are only 2 cm apart.
Sun seedlings are always taller than shade seedlings.
Based on these samples, seedlings in the sun tend to be taller on average, but heights vary more.
Explanation
Using sample medians and IQRs for an informal comparison: the center is higher in sun (14 vs 12), suggesting taller typical plants, while spread is larger in sun (IQR 4 vs 2), so there is more variability and not every plant in sun is taller.
Commute times for two bus routes were sampled. Route M (n=40): mean 22 minutes, MAD 7 minutes. Route N (n=38): mean 24 minutes, MAD 5 minutes. Which inference is most reasonable?
Route M is always faster for everyone because its mean is lower.
Based on these samples, Route M tends to have slightly shorter trips on average, but its times are more variable.
The routes are the same because the MAD values are single-digit numbers.
Route N must be faster overall because its MAD is smaller.
Explanation
This is an informal, sample-based inference. The center (mean) is lower for Route M (22 vs 24), suggesting shorter typical times, but M's spread is larger (MAD 7 vs 5), so its times are more variable and not always faster for every rider.
Two random samples recorded texts sent per day. Grade 7 (n=32): median 55 texts, IQR 18. Grade 8 (n=30): median 60 texts, IQR 30. Which inference is most reasonable?
Grade 8 students all text more than Grade 7 students because their median is higher.
The grades text the same amount because the IQRs are different.
Based on these samples, Grade 8 tends to send more texts on average, but results are more variable.
Grade 7 must send more texts because a smaller IQR always means a higher center.
Explanation
This is an informal comparison using samples. The center (median) is higher for Grade 8 (60 vs 55), suggesting a tendency toward more texts, but Grade 8's spread is larger (IQR 30 vs 18), so texting amounts are more variable and not higher for every student.