Data analysis (mean, median, mode, range; graphs) — ISEE Upper practice questions
Data analysis (mean, median, mode, range; graphs) on the ISEE Upper Quantitative Reasoning section covers the mean, median, mode, and range of a data set, overlapping groups, and reading tables or graphs. A student must recover a missing score from a given average, recompute the mean and median after a new value is added, and find how many people belong to both of two groups. Questions are short word problems whose four answer choices are usually a single count or a paired mean and median. Common traps include mixing mean with median, using the old count when a new data point is added, and double-counting those in both groups.
Section: Quantitative Reasoning 37 questions on the paper
137 practice questions in the app
Sample questions
Question 1
A group of 18 students has an average score of 84 on a quiz scored out of 110 points. After one more student takes the quiz, the average score of all 19 students is 85.
Column A
Column B
The score of the additional student
100
AThe quantity in Column A is greater
BThe quantity in Column B is greater
CThe two quantities are equal
DThe relationship cannot be determined from the information given
Show answer
Answer: A — The quantity in Column A is greater
The original total is 18×84=1512, and the new total is 19×85=1615. The added student scored 1615−1512=103, so Column A is greater.
Question 2
At a school fair, 42 students visited the art booth, the science booth, or both. Every student is included in at least one of those groups. If 25 students visited the art booth and 31 students visited the science booth, how many students visited both booths?
A10
B14
C16
D18
Show answer
Answer: B — 14
The sum 25+31=56 counts students who visited both booths twice. Since there were 42 students total, the overlap is 56−42=14.
Question 3
Five walking times, in minutes, are 12,14,15,17, and 22. A sixth walking time of 28 minutes is added to the data set. What are the mean and median of the new data set?
AThe mean is 18, and the median is 15.
BThe mean is 16, and the median is 16.
CThe mean is 18, and the median is 16.
DThe mean is 16, and the median is 15.
Show answer
Answer: C — The mean is 18, and the median is 16.
The new mean is (12+14+15+17+22+28)÷6=18. The middle values are 15 and 17, so the new median is (15+17)÷2=16.
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