Statistics and Data Displays: math test solutions, Grade 6 – download the PDF

1 Statistical questions / 3 pts

1. Not statistical: the answer is a single count (1 pt).
2. Not statistical: the answer is always 5 (1 pt).
3. Statistical: students send different numbers of messages, so there is variability (1 pt).

2 Measures of center and range / 4 pts

In order: 9, 10, 11, 12, 14, 15, 15, 15, 16.

Mean: \(117 \div 9 = 13\) (1 pt). Median: the 5th value, 14 (1 pt). Mode: 15, which appears 3 times (1 pt). Range: \(16 - 9 = 7\) (1 pt).

3 Five-number summary / 4 pts

Median: the mean of the 5th and 6th values, \(\dfrac{10+12}{2} = 11\) (1 pt). Lower half: 4, 6, 7, 9, 10, so \(Q_1 = 7\). Upper half: 12, 13, 15, 16, 20, so \(Q_3 = 15\) (1 pt).

Summary: 4, 7, 11, 15, 20 (1 pt). IQR \(= 15-7 = 8\) and range \(= 20-4 = 16\) (1 pt).

4 Mean absolute deviation / 3 pts

Mean: \(45 \div 5 = 9\) (1 pt). Distances from 9: 4, 2, 1, 1, 6 (1 pt). Sum 14, so \(\text{MAD} = 14 \div 5 = 2.8\) (1 pt).

5 Reading a histogram / 3 pts

1. \(3+7+6+4 = 20\) games (1 pt).
2. Bins 0–10 and 10–20: \(3+7 = 10\) games (1 pt).
3. The bin 30–40 has 4 games: \(\dfrac{4}{20} = \dfrac{1}{5}\) (1 pt).

6 Choosing a measure of center / 3 pts

Sum: \(12+13+13+14+15+16+43 = 126\). Mean: \(126 \div 7 = 18\) (1 pt). Median: the 4th value, 14 (1 pt).

The median is better: six of seven students took 16 minutes or less, and the single 43 minute outlier pulls the mean up (1 pt).