SAT Math Multiple Choice Question 866: Answer and Explanation
11. Brian and several of his work colleagues are on a kickball team together. The dotplot above shows the number of points his team scored during each of 14 games playedso far this season. The league's record for highest average points scored per gameduring a season is 7.5. To break this record, a team's season average must be at leasthalf a point higher. If Brian and his teammates are to set a new season record, howmany points must they average during their final two games?
- A. 9
- B. 12
- C. 14
- D. 15
Correct Answer: B
Category: Problem Solving and Data Analysis / Statistics and Probability
Strategic Advice: The average of a data set is found by adding all the values and dividing the result by the number of values. Use this information in reverse to answer a question like this.
Getting to the Answer: The question implies that there are 16 games per season (Brian's team has already played 14 and has 2 left) and that Brian's team must average 8 points (the current record, 7.5, plus half a point) per game to beat the old record. To average 8 points per game, a team must score a total of 8 × 16 = 128 points during the season. Each '×' on the dot plot represents one game, so Brian's team has already scored a total of (2 × 4) + 5 + (3 × 6) + 7 + 8 + (3 × 9) + (2 × 10) + 11 = 104 points. They are currently 24 points short of the 8-point average with two games left to play, which means they must average at least 12 points per game during their last two games. (B) is the correct answer.