Study on the flyISEE UpperQuantitative ReasoningData analysis (mean, median, mode, range; graphs)
Quantitative Reasoning
Mean, median, mode and range each describe data differently, and Data analysis (mean, median, mode, range; graphs) checks that difference.
Adding one very large value raises the mean noticeably but moves the median only a little, a contrast often tested by asking for both measures after a new value joins the set. Average problems are easiest through totals: the mean times the count gives the sum, so a new average reveals the added value.
Overlap questions use a two-circle Venn diagram, where people in both groups must be subtracted once. Graph questions ask for readings from bar or line charts, so axis labels need checking first.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Mid
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 |
Answer: A — The quantity in Column A is greater
The original total is , and the new total is . The added student scored , so Column A is greater.
Question 2Easier
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?
Answer: B — 14
The sum counts students who visited both booths twice. Since there were 42 students total, the overlap is .
Question 3Easier
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?
Answer: C — The mean is 18, and the median is 16.
The new mean is . The middle values are 15 and 17, so the new median is .
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Harder than the exam: ISEE Upper Challenge · Competition-style problems
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