Data analysis and probability — ISEE Upper practice questions

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Practice 328 Data analysis and probability questions in the app

What this topic is

Data analysis and probability in Mathematics Achievement goes beyond basic averages.

Expected value is one idea met here: multiply each outcome by its probability and add the results. The probability of one event or another requires adding the two probabilities and subtracting the chance that both happen, so no outcome is counted twice. Overlapping groups use Venn diagrams, sometimes with three circles, where finding those in exactly one group means removing every overlap.

Other items read data from tables, bar graphs or stem-and-leaf plots and ask for the mean, median, mode or range. Choices often contain the total before overlaps were removed.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

A fair six-sided number cube is rolled twice. What is the probability that the sum of the two rolls is 9 or the product of the two rolls is 20?

\frac{1}{18}

✗ Not this one

\frac{1}{12}

✗ Not this one

\frac{1}{9}

✓ Correct

\frac{1}{6}

✗ Not this one

Show answer

Answer: C — $\frac{1}{9}$

The pairs with sum 9 are $(3, 6), (4, 5), (5, 4),$ and $(6, 3)$ . The pairs with product 20 are $(4, 5)$ and $(5, 4)$ , which are already included. There are 4 favorable outcomes out of 36, so the probability is $\frac{4}{36} = \frac{1}{9}$ .

Question 2Harder

A reward system gives exactly one of three point awards. The probability of receiving 2 points is $20 %$ , and the probability of receiving 10 points is $25 %$ . All remaining participants receive 6 points. What is the expected number of points received?

2.90✗ Not this one6.00✗ Not this one6.20✓ Correct8.90✗ Not this one

Show answer

Answer: C — 6.20

The probability of receiving 6 points is $100 % - 20 % - 25 % = 55 %$ . Thus, the expected value is $2 (0.20) + 6 (0.55) + 10 (0.25) = 6.20$ .

Question 3Harder

At a school, 27 students belong to the robotics club, 23 belong to the debate club, and 19 belong to the art club. The pairwise overlaps are 10, 8, and 7, and each includes the 3 students who belong to all three clubs. How many students belong to exactly one of the three clubs?

16✗ Not this one19✗ Not this one28✓ Correct47✗ Not this one

Show answer

Answer: C — 28

The pair-only regions contain $(10 - 3) + (8 - 3) + (7 - 3) = 16$ students. Since there are 69 club memberships total, the number in exactly one club is $69 - 2 (16) - 3 (3) = 28$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 328 Data analysis and probability questions in the app

Data analysis and probability — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement