1. Problem: Find the mean of the number of cars sold in the past 10 days: 1, 5, 3, 2, 1, 0, 4, 2, 6, 1. Formula: Mean $= \frac{\text{sum of all values}}{\text{number of values}}$ Calculation: Sum $= 1+5+3+2+1+0+4+2+6+1=25$ Number of values $=10$ Mean $= \frac{25}{10} = 2.5$ 2. Problem: Find the mean of utility bills for the past 6 months: 90, 120, 140, 135, 112, 126. Sum $= 90+120+140+135+112+126=723$ Number of values $=6$ Mean $= \frac{723}{6} = 120.5$ 3. Problem: Find the mean price of a sweater in 5 different stores: 31.25, 27.50, 28.00, 36.95, 32.10. Sum $= 31.25+27.50+28.00+36.95+32.10=155.8$ Number of values $=5$ Mean $= \frac{155.8}{5} = 31.16$ 4. Problem: Find the mean score on a 10-point quiz: 7, 9, 10, 8, 4, 2, 6, 10, 8. Sum $= 7+9+10+8+4+2+6+10+8=64$ Number of values $=9$ Mean $= \frac{64}{9} \approx 7.11$ 5. Problem: Find the mean hourly wage: 7.25, 6.75, 8.10, 9.56, 7.10, 7.75. Sum $= 7.25+6.75+8.10+9.56+7.10+7.75=46.51$ Number of values $=6$ Mean $= \frac{46.51}{6} \approx 7.75$ 6. Problem: Find the mean age of students on the quiz team: 15, 15, 14, 16, 17, 16, 16, 15. Sum $= 15+15+14+16+17+16+16+15=124$ Number of values $=8$ Mean $= \frac{124}{8} = 15.5$ 7. Problem: Find $x$ if mean of 4.8, 1.6, 5.2, $x$ is 3.7. Formula: $\frac{4.8+1.6+5.2+x}{4} = 3.7$ Multiply both sides by 4: $4.8+1.6+5.2+x = 14.8$ Sum known values: $4.8+1.6+5.2=11.6$ Solve for $x$: $x = 14.8 - 11.6 = 3.2$ 8. Problem: Find $x$ if mean of 40, 98, 94, 102, 21, $x$ is 88. $\frac{40+98+94+102+21+x}{6} = 88$ Sum known values: $40+98+94+102+21=355$ Multiply both sides by 6: $355 + x = 528$ Solve for $x$: $x = 528 - 355 = 173$ 9. Problem: Find $x$ if mean of 100, 172, 85, 92, $x$ is 115. $\frac{100+172+85+92+x}{5} = 115$ Sum known values: $100+172+85+92=449$ Multiply both sides by 5: $449 + x = 575$ Solve for $x$: $x = 575 - 449 = 126$ 10. Problem: Find $x$ if mean of 25.6, 19.3, 19, $x$ is 24. $\frac{25.6+19.3+19+x}{4} = 24$ Sum known values: $25.6+19.3+19=63.9$ Multiply both sides by 4: $63.9 + x = 96$ Solve for $x$: $x = 96 - 63.9 = 32.1$ 11. Problem: Compare average strikeouts against Boston and St. Louis. Boston strikeouts: 1, 2, 4, 2, 1, 3, 3, 0 Sum Boston $= 1+2+4+2+1+3+3+0=16$ Number of games Boston $=8$ Mean Boston $= \frac{16}{8} = 2$ St. Louis strikeouts: 3, 1, 2, 3, 2 Sum St. Louis $= 3+1+2+3+2=11$ Number of games St. Louis $=5$ Mean St. Louis $= \frac{11}{5} = 2.2$ Conclusion: Pitcher averaged more strikeouts against St. Louis. 12. Problem: Find grade needed on next test for average 92 given grades 85, 92, 96, 89. Let $x$ be the needed grade. $\frac{85+92+96+89+x}{5} = 92$ Sum known grades: $85+92+96+89=362$ Multiply both sides by 5: $362 + x = 460$ Solve for $x$: $x = 460 - 362 = 98$ 13. Problem: Did the car pass the exhaust test with samples 8, 5, 7, 6, 9, 5 and max mean 6 ppm? Sum $= 8+5+7+6+9+5=40$ Number of samples $=6$ Mean $= \frac{40}{6} \approx 6.67$ Since $6.67 > 6$, the car did not pass the test. 14. Problem: Is the coffee machine reliable if range < 2 fl oz for amounts 7.1, 6.8, 7.6, 7.1, 7.4, 6.8, 7, 6.7? Range $= \text{max} - \text{min} = 7.6 - 6.7 = 0.9$ Since $0.9 < 2$, the machine is reliable. 15. Problem: Did the show make a profit if average tickets sold per show is at least 1100? Tickets sold: 1000, 800, 1600, 900, 1200, 900, 800, 1700, 900, 1200, 1000, 1200 Sum $= 1000+800+1600+900+1200+900+800+1700+900+1200+1000+1200=13300$ Number of shows $=12$ Mean $= \frac{13300}{12} \approx 1108.33$ Since $1108.33 \geq 1100$, the show made a profit. 16a. Problem: Make a stem-and-leaf plot for bread loaves sold: 43, 39, 17, 38, 50, 42, 34, 28, 37, 42, 40, 33, 72, 36, 45, 21, 29, 44, 41, 37, 40, 35, 51, 54. 16b. Find mean, median, mode, range. Sorted data: 17, 21, 28, 29, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 50, 51, 54, 72 Sum $= 17+21+28+29+33+34+35+36+37+37+38+39+40+40+41+42+42+43+44+45+50+51+54+72= 1004$ Number of values $=24$ Mean $= \frac{1004}{24} \approx 41.83$ Median: average of 12th and 13th values: (39 + 40)/2 = 39.5 Mode: 37, 40, 42 (each appears twice) Range: $72 - 17 = 55$ 17a. Problem: Make a stem-and-leaf plot for calls to police: 32, 42, 35, 52, 58, 52, 46, 61, 52, 63, 81, 61, 63, 39, 41, 48, 62, 61, 58, 34, 49, 47, 49, 31. 17b. Find mean, median, mode, range. Sorted data: 31, 32, 34, 35, 39, 41, 42, 46, 47, 48, 49, 49, 52, 52, 52, 58, 58, 61, 61, 61, 62, 63, 63, 81 Sum $= 31+32+34+35+39+41+42+46+47+48+49+49+52+52+52+58+58+61+61+61+62+63+63+81= 1305$ Number of values $=24$ Mean $= \frac{1305}{24} \approx 54.38$ Median: average of 12th and 13th values: (49 + 52)/2 = 50.5 Mode: 52 and 61 (each appears 3 times) Range: $81 - 31 = 50$