1. Calculate the mean for the following data sets. **a.** Data: 11, 10, 12, 12, 9, 10, 14, 12, 9 - Step 1: Sum the numbers: $$11 + 10 + 12 + 12 + 9 + 10 + 14 + 12 + 9 = 99$$ - Step 2: Count the numbers: 9 - Step 3: Calculate mean: $$\frac{99}{9} = 11$$ **b.** Data: 18, 15, 19, 16, 15 - Step 1: Sum: $$18 + 15 + 19 + 16 + 15 = 83$$ - Step 2: Count: 5 - Step 3: Mean: $$\frac{83}{5} = 16.6$$ **c.** Data: 11, 13, 16, 12, 12, 14 - Step 1: Sum: $$11 + 13 + 16 + 12 + 12 + 14 = 78$$ - Step 2: Count: 6 - Step 3: Mean: $$\frac{78}{6} = 13$$ **d.** Data: 21, 30, 22, 16, 24, 28, 16, 17 - Step 1: Sum: $$21 + 30 + 22 + 16 + 24 + 28 + 16 + 17 = 174$$ - Step 2: Count: 8 - Step 3: Mean: $$\frac{174}{8} = 21.75$$ **e.** Data: 108, 99, 112, 111, 108 - Step 1: Sum: $$108 + 99 + 112 + 111 + 108 = 538$$ - Step 2: Count: 5 - Step 3: Mean: $$\frac{538}{5} = 107.6$$ **f.** Data: 12, 14, 15, 17, 15 - Step 1: Sum: $$12 + 14 + 15 + 17 + 15 = 73$$ - Step 2: Count: 5 - Step 3: Mean: $$\frac{73}{5} = 14.6$$ **g.** Data: 5, 7, 3, 5, 8, 9, 10, 2 - Step 1: Sum: $$5 + 7 + 3 + 5 + 8 + 9 + 10 + 2 = 49$$ - Step 2: Count: 8 - Step 3: Mean: $$\frac{49}{8} = 6.125$$ **h.** Data: 30, 20, 24, 32 - Step 1: Sum: $$30 + 20 + 24 + 32 = 106$$ - Step 2: Count: 4 - Step 3: Mean: $$\frac{106}{4} = 26.5$$ **i.** Data: 9, -3, -6, 5, 0 (correcting the input) - Step 1: Sum: $$9 + (-3) + (-6) + 5 + 0 = 5$$ - Step 2: Count: 5 - Step 3: Mean: $$\frac{5}{5} = 1$$ **j.** Data: -5, 1, 3, 6, -8, 1 - Step 1: Sum: $$-5 + 1 + 3 + 6 + (-8) + 1 = -2$$ - Step 2: Count: 6 - Step 3: Mean: $$\frac{-2}{6} = -0.3333$$ 2. Calculate the mean for the following decimal data sets. **a.** Data: 1.6, 2.0, 1.4, 1.8, 1.2, 1.4, 1.9 - Step 1: Sum: $$1.6 + 2.0 + 1.4 + 1.8 + 1.2 + 1.4 + 1.9 = 11.3$$ - Step 2: Count: 7 - Step 3: Mean: $$\frac{11.3}{7} \approx 1.614$$ **b.** Data: 2.3, 2.6, 2.8, 2.7, 2.8, 2.7, 2.4, 2.3, 2.1, 2.3 (correcting 2-8 to 2.8 and adding missing commas) - Step 1: Sum: $$2.3 + 2.6 + 2.8 + 2.7 + 2.8 + 2.7 + 2.4 + 2.3 + 2.1 + 2.3 = 24.0$$ - Step 2: Count: 10 - Step 3: Mean: $$\frac{24.0}{10} = 2.4$$ **c.** Data: 1.4, 2.8, 2.4, 2.5, 2.8, 3.1, 1.1 - Step 1: Sum: $$1.4 + 2.8 + 2.4 + 2.5 + 2.8 + 3.1 + 1.1 = 16.1$$ - Step 2: Count: 7 - Step 3: Mean: $$\frac{16.1}{7} \approx 2.3$$ **d.** Data: 1.0, 1.2, 1.0, 1.7, 1.1 (correcting 1-1 to 1.1) - Step 1: Sum: $$1.0 + 1.2 + 1.0 + 1.7 + 1.1 = 6.0$$ - Step 2: Count: 5 - Step 3: Mean: $$\frac{6.0}{5} = 1.2$$ **e.** Data: 3.4, 3.8, 3.8, 2.2, 2.4 - Step 1: Sum: $$3.4 + 3.8 + 3.8 + 2.2 + 2.4 = 15.6$$ - Step 2: Count: 5 - Step 3: Mean: $$\frac{15.6}{5} = 3.12$$ **f.** Data: 4.3, 3.2, 3.1, 4.3, 2.1, 2.3, 1.7 (correcting missing commas) - Step 1: Sum: $$4.3 + 3.2 + 3.1 + 4.3 + 2.1 + 2.3 + 1.7 = 21.0$$ - Step 2: Count: 7 - Step 3: Mean: $$\frac{21.0}{7} = 3.0$$ **g.** Data: 5.0, 5.1, 5.2, 5.2, 5.6, 5.7, 6.0, 6.2 (correcting 5-6, 5-7, 6-0, 6-2 to decimals) - Step 1: Sum: $$5.0 + 5.1 + 5.2 + 5.2 + 5.6 + 5.7 + 6.0 + 6.2 = 43.0$$ - Step 2: Count: 8 - Step 3: Mean: $$\frac{43.0}{8} = 5.375$$ **h.** Data: 4.0, 4.5, 5.0, 5.5, 6.0, 7.5 - Step 1: Sum: $$4.0 + 4.5 + 5.0 + 5.5 + 6.0 + 7.5 = 32.5$$ - Step 2: Count: 6 - Step 3: Mean: $$\frac{32.5}{6} \approx 5.42$$ **i.** Data: 5.0, 1.2, 1.3, 1.6, 1.2, 1.4, 1.2, 5.0, 1.0 (correcting 14 to 1.4 and 1-2 to 1.2, 5-0 to 5.0) - Step 1: Sum: $$5.0 + 1.2 + 1.3 + 1.6 + 1.2 + 1.4 + 1.2 + 5.0 + 1.0 = 18.9$$ - Step 2: Count: 9 - Step 3: Mean: $$\frac{18.9}{9} = 2.1$$ 3. Calculate the mean price of petrol at 6 garages: 76, 75, 76, 477, 78, 179 - Step 1: Sum: $$76 + 75 + 76 + 477 + 78 + 179 = 961$$ - Step 2: Count: 6 - Step 3: Mean: $$\frac{961}{6} \approx 160.17$$ **Final answers:** 1a. 11 1b. 16.6 1c. 13 1d. 21.75 1e. 107.6 1f. 14.6 1g. 6.125 1h. 26.5 1i. 1 1j. -0.3333 2a. 1.614 2b. 2.4 2c. 2.3 2d. 1.2 2e. 3.12 2f. 3.0 2g. 5.375 2h. 5.42 2i. 2.1 3. 160.17