Data & Statistics (Advanced)

Harder items at competition-adjacent depth.

Phase 2 · SAT Math

Data & Statistics: core idea

Compare distributions.

The mean of $10$ values is $24$ . One value, recorded as $19$ , should have been $29$ . What is the corrected mean?

Hint: The total rises by 10. Answer: 25.

1. A box has $4$ red, $3$ blue, and $5$ white balls. Two are drawn without replacement. What is the probability both are red?
2. A line of best fit has residual $-3$ for a point whose actual $y$ is $14$ . What is its predicted $y$ ?
3. In a normal distribution with mean $70$ and standard deviation $8$ , what is the z-score of $86$ ?
4. A school randomly samples $100$ of $800$ students; $28$ prefer buses. Give the estimated number preferring buses.
5. Events $A$ and $B$ have $P(A)=0.6$ , $P(B)=0.5$ , and $P(A\cap B)=0.3$ . Find $P(A\cup B)$ .
6. For values $1,2,3,4,20$ , which measure is most affected by the outlier 20?
7. A game wins $4$ points with probability $0.3$ and loses $1$ point otherwise. What is the expected score?
8. A data set has $Q_1=10$ , $Q_3=18$ . Using the $1.5\text{ IQR}$ rule, values above what number are outliers?
9. Two independent fair dice are rolled. What is the probability their sum is $9$ ?