AP Statistics 1.7 Summary Statistics for One Quantitative Variable- Exam Style Questions - MCQs - New Syllabus
▶️ Answer/Explanation
There are 57 earthquakes, so the median is the 29th observation when the data are ordered from smallest to largest.
\(\text{Median Position}=\frac{57+1}{2}=29\)
From the histogram, approximately 2 earthquakes fall in the interval 0.5–1.0 and about 17 fall in 1.0–1.5, giving a cumulative count of about 19. The next interval, 1.5–2.0, contains about 13 earthquakes, bringing the cumulative count to about 32.
Since the 29th observation falls within the interval 1.5–2.0, the median magnitude must lie in that class interval.
✅ Answer: (B)
▶️ Answer/Explanation
The first quartile (Q1) is 43 inches and the third quartile (Q3) is 48 inches. By definition, the interval from Q1 to Q3 contains the middle 50% of the observations.
Since the sample size is 200 children:
\( 50\% \times 200 = 100 \)
Therefore, approximately 100 children have heights between 43 inches and 48 inches. The other choices correspond to different percentages of the distribution and cannot be determined to be about 100 children from the information given.
✅ Answer: (C)
▶️ Answer/Explanation
The means and medians of the two separate samples do not provide enough information to determine the median of the combined data set.
To find the median of the combined sample of 47 observations, we would need to know the actual ordering of all 47 values. Different data sets can have the same sample sizes, means, and medians but produce different combined medians.
While choice (C) correctly computes the combined mean, none of the formulas shown can be used to determine the combined median from the information given.
Therefore, the median of the combined sample cannot be determined.
✅ Answer: (E)