Question

directions. find the average (mean) for each set of numbers. round to the nearest tenth if necessary
part a: basic averages (1 point each)

1. 4, 6, 8
2. 12, 15, 18
3. 7, 10, 13, 16
4. 2, 3, 5, 10
5. 25, 30, 35, 40
6. 9, 11, 14, 16
7. 5, 8, 12, 15, 20
8. 50, 60, 70
9. 3, 9, 12
10. 4, 7, 9, 11

part b: slightly harder sets

1. 14, 18, 22, 26, 30
2. 5, 10, 15, 25
3. 45, 55, 65, 75
4. 3.5, 4.5, 5.5, 6.5
5. 120, 135, 150, 165
6. 9, 8, 10, 7, 6

part c: word problems

1. three students scored 75, 85, and 90 on a quiz. what is their average score?
2. a car travels 120 miles, 150 miles, and 130 miles over three days. what is the average distance traveled per day?
3. the temperatures for four days were 68°f, 70°f, 72°f, and 74°f. find the average temperature.
4. sarah had test scores of 88, 92, 84, and 96. what is her average test score?

challenge (optional bonus): the average of four numbers is 20. three of the numbers are 15, 22, and 25. what is the fourth number?

Explanation:

Step1: Calculate the sum of numbers

For each set, add all the numbers together.
For example, for set 1: \(4 + 6+8=18\)
For set 2: \(12 + 15+18 = 45\)
For set 3: \(7+10 + 13+16=46\)
For set 4: \(2+3 + 5+10=20\)
For set 5: \(25+30 + 35+40 = 130\)
For set 6: \(9+11 + 14+16=50\)
For set 7: \(5+8 + 12+15+20=60\)
For set 8: \(50+60 + 70=180\)
For set 9: \(3+9 + 12=24\)
For set 10: \(4+7 + 9+11=31\)
For set 11: \(14+18 + 22+26+30=110\)
For set 12: \(5+10 + 15+25=55\)
For set 13: \(45+55 + 65+75=240\)
For set 14: \(3.5+4.5 + 5.5+6.5=20\)
For set 15: \(120+135 + 150+165=570\)
For set 16: \(9+8 + 10+7+6=40\)
For problem 17: \(75 + 85+90=250\)
For problem 18: \(120+150 + 130=400\)
For problem 19: \(68+70 + 72+74=284\)
For problem 20: \(88+92 + 84+96=360\)
For challenge problem 25: Let the fourth number be \(x\). The sum of the four numbers is \(20\times4=80\). The sum of the three known numbers is \(15 + 22+25=62\). So \(x=80 - 62=18\)

Step2: Divide by the number of elements

For set 1: \(\frac{18}{3}=6\)
For set 2: \(\frac{45}{3}=15\)
For set 3: \(\frac{46}{4}=11.5\)
For set 4: \(\frac{20}{4}=5\)
For set 5: \(\frac{130}{4}=32.5\)
For set 6: \(\frac{50}{4}=12.5\)
For set 7: \(\frac{60}{5}=12\)
For set 8: \(\frac{180}{3}=60\)
For set 9: \(\frac{24}{3}=8\)
For set 10: \(\frac{31}{4}=7.75\approx7.8\)
For set 11: \(\frac{110}{5}=22\)
For set 12: \(\frac{55}{4}=13.75\approx13.8\)
For set 13: \(\frac{240}{4}=60\)
For set 14: \(\frac{20}{4}=5\)
For set 15: \(\frac{570}{4}=142.5\)
For set 16: \(\frac{40}{5}=8\)
For problem 17: \(\frac{250}{3}\approx83.3\)
For problem 18: \(\frac{400}{3}\approx133.3\)
For problem 19: \(\frac{284}{4}=71\)
For problem 20: \(\frac{360}{4}=90\)
For challenge problem 25: \(x = 18\)

Answer:

1. \(6\)
2. \(15\)
3. \(11.5\)
4. \(5\)
5. \(32.5\)
6. \(12.5\)
7. \(12\)
8. \(60\)
9. \(8\)
10. \(7.8\)
11. \(22\)
12. \(13.8\)
13. \(60\)
14. \(5\)
15. \(142.5\)
16. \(8\)
17. \(83.3\)
18. \(133.3\)
19. \(71\)
20. \(90\)
21. \(18\)