Digital PSAT Math Practice Question 287: Answer and Explanation

Question: 287

A teacher gives a five-question pop quiz, and students can score any whole value between 0 and 5, inclusive.

In the above set of quiz results, which of these quantities would be greatest?

• A. The median quiz score
• B. The mean quiz score
• C. The mode of the quiz scores
• D. The mean and median will be tied for the greatest value.

Correct Answer: C

Explanation:

(C) The mode is the quantity that occurs most frequently. Looking at the table, 8 students scored 5 points on the quiz, while fewer than 8 students scored each of the other 5 possible point values. Thus, the mode of the quiz scores is 5 since this is the score that occurred most frequently. Eyeballing the data, it is likely that the median (the middle value) and the mean (the average) are both less than 5, the highest possible score, so you could deduce that the answer is choice (C). But, find the median and mean as well to confirm that the mode is indeed the greatest quantity in this data set. To find the median, you arrange all students' scores from lowest to highest and choose the score in the middle. From the chart, you can see that there are 29 students, so the median will be the score of the 15th student. Going in order from lowest to highest score, there were 2 students who scored 0 points, 3 students who scored 1 point, 6 students who scored 2 points, and 7 students who scored 3 points. In other words, the first 11 students scored 2 points or less, and then the next 7 students all scored 3 points. In particular, the 15th student must have scored 3 points, so the median is 3.

To find the mean, you take the sum of all students' scores and divide by the total number of students. You get

Thus, the mean and the median are both less than 5, so the mode is the highest quantity.