1. **Find the median for each set of data.** Median is the middle value when data is ordered from least to greatest. If there is an even number of data points, median is the average of the two middle numbers. A. Data: 49, 32, 67, 55, 58 Ordered: 32, 49, 55, 58, 67 Median is the middle value: $55$ B. Data: 3.1, 5.2, 4.4, 5.0, 3.8, 2.6, 4.7 Ordered: 2.6, 3.1, 3.8, 4.4, 4.7, 5.0, 5.2 Median is the middle value: $4.4$ C. Data: 29, 12, 30, 22, 7, 23, 36, 15, 18, 9 Ordered: 7, 9, 12, 15, 18, 22, 23, 29, 30, 36 Even number of values (10), median is average of 5th and 6th: $$\frac{18 + 22}{2} = \frac{40}{2} = 20$$ D. Data: 81.6, 83.7, 78.5, 82.8, 81.2, 76.3, 83.5, 78.9 Ordered: 76.3, 78.5, 78.9, 81.2, 81.6, 82.8, 83.5, 83.7 Even number (8), median is average of 4th and 5th: $$\frac{81.2 + 81.6}{2} = \frac{162.8}{2} = 81.4$$ E. Data: 110, 115, 109, 110, 116, 113, 112, 116, 110, 106, 113 Ordered: 106, 109, 110, 110, 110, 112, 113, 113, 115, 116, 116 Odd number (11), median is 6th value: $112$ F. Prices: 41.75, 43.89, 42.50, 43.40, 42.95, 39.95, 42.90, 40.50, 40.69, 39.95, 45.30, 42.95 Ordered: 39.95, 39.95, 40.50, 40.69, 41.75, 42.50, 42.90, 42.95, 42.95, 43.40, 43.89, 45.30 Even number (12), median is average of 6th and 7th: $$\frac{42.50 + 42.90}{2} = \frac{85.4}{2} = 42.7$$ 2. **Weekly salaries for 5 people.** A. Mean salary is sum divided by number of people. Salaries: 45000, 2000, 1500, 1100, 400 Sum: $45000 + 2000 + 1500 + 1100 + 400 = 50000$ Mean: $$\frac{50000}{5} = 10000$$ B. Median salary is middle value when ordered: Ordered: 400, 1100, 1500, 2000, 45000 Median is 3rd value: $1500$ 3. **Find the mode(s) for each set of data.** Mode is the value(s) that appear most frequently. A. Suit Sizes (all values combined): 36, 39, 40, 37, 39, 41, 37, 39, 41, 38, 40, 41, 38, 40, 42, 38, 40, 44, 39, 40, 44 Count frequencies: - 39 appears 4 times - 40 appears 6 times - 38 appears 3 times - 41 appears 3 times - Others less Mode: $40$ B. Times in 50-m Dash (seconds): Values combined: 5.7, 6.3, 6.7, 6.9, 5.9, 6.3, 6.7, 7.0, 6.0, 6.4, 6.8, 7.2, 6.0, 6.5, 6.9, 7.3, 6.2, 6.5, 6.9, 7.3, 6.3, 6.7, 6.9, 7.5 Count frequencies: - 6.9 appears 4 times - 6.3 appears 3 times - 6.7 appears 3 times - 6.0 appears 2 times - 6.5 appears 2 times - 7.3 appears 2 times Mode: $6.9$ C. Runs Scored: Values combined: 3,7,2,8,4,1,4,0,5,7,2,2,1,1,5,7,1,5,6,7,0,5,3,2,2,6,4,9,5,9 Count frequencies: - 5 appears 5 times - 7 appears 5 times - 2 appears 5 times Mode: $2, 5, 7$ 4. **Typing speeds for 12 students.** Speeds: 31, 30, 27, 24, 15, 18, 31, 35, 24, 28, 13, 24 A. Range = max - min = $35 - 13 = 22$ B. Mean = sum / 12 Sum: $31 + 30 + 27 + 24 + 15 + 18 + 31 + 35 + 24 + 28 + 13 + 24 = 300$ Mean: $$\frac{300}{12} = 25$$ C. Median: order speeds: 13, 15, 18, 24, 24, 24, 27, 28, 30, 31, 31, 35 Even number (12), median is average of 6th and 7th: $$\frac{24 + 27}{2} = \frac{51}{2} = 25.5$$ D. Mode(s): value(s) appearing most frequently 24 appears 3 times 31 appears 2 times Mode: $24$ Final answers: 1A: 55 1B: 4.4 1C: 20 1D: 81.4 1E: 112 1F: 42.7 2A: 10000 2B: 1500 3A: 40 3B: 6.9 3C: 2, 5, 7 4A: 22 4B: 25 4C: 25.5 4D: 24