This answer key gives a full worked solution and a scoring guide for each of the eight questions. The test is worth 20 points. Award partial credit as described, and accept any correct reasoning when a question asks which measure is best for data with an outlier.
Question 1: Mean and median (2 points)
Mean: \(\frac{6 + 3 + 12 + 8 + 5 + 14}{6} = \frac{48}{6} = 8\).
Order: 3, 5, 6, 8, 12, 14. Median: \(\frac{6 + 8}{2} = 7\).
The mean is 8 and the median is 7.
Scoring: 1 point for the mean; 1 point for ordering the data and finding the median.
Question 2: Range and IQR (2 points)
Order: 11, 12, 14, 17, 19, 20, 23, 25.
Range: \(25 – 11 = 14\).
Median: \(\frac{17 + 19}{2} = 18\). \(Q_1 = \frac{12 + 14}{2} = 13\). \(Q_3 = \frac{20 + 23}{2} = 21.5\).
\(IQR = 21.5 – 13 = 8.5\)
The range is 14 and the IQR is 8.5.
Scoring: 1 point for the range; 1 point for the IQR.
Question 3: Mean absolute deviation (3 points)
(a) \(\frac{4 + 5 + 8 + 9 + 9}{5} = \frac{35}{5} = 7\). The mean is 7.
(b) Distances from 7: 3, 2, 1, 2, 2. Sum: 10. \(MAD = 10 : 5 = 2\). The MAD is 2.
Scoring: Part (a): 1 point. Part (b): 1 point for the distances, 1 point for the MAD.
Question 4: Missing test score (3 points)
(a) The five scores must total \(5 \times 84 = 420\). The four scores total \(80 + 90 + 78 + 88 = 336\). \(420 – 336 = 84\). The fifth score is 84.
(b) \(\frac{336 + 100}{5} = \frac{436}{5} = 87.2\). The mean is 87.2.
Scoring: Part (a): 1 point for the needed total, 1 point for the score. Part (b): 1 point.
Question 5: Yard sale prices (3 points)
(a) Mean: \(\frac{2 + 3 + 3 + 4 + 5 + 5 + 41}{7} = \frac{63}{7} = 9\). The 4th ordered value is 4, so the median is 4. The mean is \(\$9\) and the median is \(\$4\).
(b) The median is better. The price \(\$41\) is an outlier that pulls the mean above six of the seven prices.
Scoring: Part (a): 1 point each. Part (b): 1 point for choosing the median with a reason.
Question 6: Compare two teams (2 points)
Team A distances from 10: 2, 1, 0, 1, 2. Sum: 6. \(MAD = 6 : 5 = 1.2\).
Team B distances from 10: 6, 3, 0, 3, 6. Sum: 18. \(MAD = 18 : 5 = 3.6\).
The MADs are 1.2 for Team A and 3.6 for Team B.
Scoring: 1 point for each team.
Question 7: Reading a box plot (3 points)
(a) \(IQR = 34 – 20 = 14\).
(b) Range: \(52 – 12 = 40\).
(c) The values above \(Q_3 = 34\) are the top fourth of the data, which is \(\frac{1}{4}\) of the students.
Answers: 14 minutes, 40 minutes, \(\frac{1}{4}\).
Scoring: 1 point for each part.
Question 8: Salaries (2 points)
Mean: \(\frac{32 + 34 + 35 + 36 + 163}{5} = \frac{300}{5} = 60\), so \(\$60{,}000\).
Median: the 3rd value, \(\$35{,}000\).
The median, \(\$35{,}000\), is better. The salary \(\$163{,}000\) is an outlier, and four of the five workers earn far less than the mean.
Scoring: 1 point for both values; 1 point for choosing the median with a reason.
20 points
See every chapter on the Grade 6 math page.