Question

ten students took a math quiz that consisted of 10 questions. the median score was 5.5. the modal score was 6. the teacher recorded the results of the first nine students in the following line plot.

(line plot with xs at 2, 3, 4 (two xs), 5, 6 (two xs), 9, 10)

20.i. what was the average score of the first nine students whose scores were represented on the line plot? give your answer to one decimal place.
(a) 4.9
(b) 5.4
(c) 5.5
(d) 5.7

1. i. what score did the tenth student get in the quiz?

(a) 4
(b) 5
(c) 6
(d) 7

Explanation:

20.i.

Step1: Count scores from line plot

Score 2: 1 student, Score 3: 1, Score 4: 2, Score 5: 1, Score 6: 2, Score 9: 1, Score 10: 1.

Step2: Calculate total score

Total = \(2\times1 + 3\times1 + 4\times2 + 5\times1 + 6\times2 + 9\times1 + 10\times1\)
= \(2 + 3 + 8 + 5 + 12 + 9 + 10\) = \(49\)

Step3: Find average

Average = \(\frac{49}{9} \approx 5.4\) (to 1 decimal)

Step1: Recall median for 10 students

Median is average of 5th and 6th scores (sorted). First 9 scores (sorted): 2,3,4,4,5,6,6,9,10. Let 10th score be \(x\). Sorted 10 scores: 2,3,4,4,5,\(x\),6,6,9,10 (or adjusted). Median = 5.5 = \(\frac{5 + x}{2}\) (since 5th is 5, 6th is \(x\) when sorted properly).

Step2: Solve for \(x\)

\(5 + x = 11\) → \(x = 6\). Check modal score: original 9 scores have mode 4 and 6 (2 each). Adding 6 makes mode 6 (3 times), which matches modal score 6.

Answer:

B. 5.4

21.