Standard deviation
Grade 9 Math Worksheet
Circle the best answer.
Pia compares quiz scores from two classes. Class A: mean 78, SD 4. Class B: mean 78, SD 12. Which statement do the summaries support?
- Both classes average 78, but Class B's scores are more spread out.
- Class B did better, because its standard deviation is larger.
- Class A's scores are more spread out, because its SD of 4 is smaller.
- The classes did equally well, so their scores look alike.
Noah can leave 25 minutes before class. Route A: mean 20 minutes, SD 8. Route B: mean 22 minutes, SD 2. Which route is safer for arriving on time?
- Route A, because its mean time of 20 minutes is shorter than Route B's mean of 22.
- Route A, because a larger SD means faster trips, so its trips will be shorter.
- Route A, because its larger SD means steadier trips that rarely run past 25 minutes.
- Route B: trips average 2 minutes longer but stay near 22, so it is rarely late.
Esme wants plants of nearly equal height. Fertilizer X: mean growth 12 cm, SD 1. Fertilizer Y: mean growth 12 cm, SD 5. Which should Esme use?
- Either one, because the two means are equal, so the plants will be alike.
- Fertilizer X: the same average growth, but heights stay closer together.
- Fertilizer Y, because its SD of 5 means heights stay closer together.
- Fertilizer Y, because a larger SD means taller plants.
Milo wants the more consistent team. Team A: mean 14 points, SD 2. Team B: mean 17 points, SD 9. Which team is more consistent?
- Team B is more consistent, because its larger SD means steadier scores.
- Team B is more consistent, because a larger SD means better scores.
- Team A is more consistent, even though Team B scores more on average.
- Team B is more consistent, because its mean of 17 is higher.
Jun's water temperatures have an SD of 2.5 °C. Converting with F = 1.8 × C + 32, what is the SD in °F?
- 4.5 °F
- 8.1 °F
- 2.5 °F
- 36.5 °F
A teacher adds 5 points to every score. Before, the mean was 71 and the SD was 6.2. Ren asks: what is the SD after the curve?
- 6.2
- 11.2
- 31
- 76
Read this first
Pia
Score 94 on a test with mean 80, SD 7. Bo: score 84 on a test with mean 70, SD 4.
Zee compares scores on two different tests. Whose score stands higher compared with its own test's mean and SD?
- They are equal, because each score is 14 points above its mean.
- Pia, because 94 is higher than 84, so Pia stands higher on a test.
- Pia, because the SD of 7 is larger than 4, so Pia has more room above the mean.
- Bo: 84 is 3.5 SDs above its mean, while Pia's 94 is 2 SDs above.
Kira
150 cm in a row with mean 120 cm, SD 15 cm. Zee: 70 cm in a row with mean 50 cm, SD 5 cm.
Luz compares sunflowers from two different rows. Which sunflower is taller compared with its own row's mean and SD?
- Kira, because 150 cm is taller than 70 cm, so Kira's sunflower stands higher.
- Kira, because the SD of 15 is larger than 5, so Kira has more room above the mean.
- Zee: 70 cm is 4 SDs above its mean, while Kira's 150 cm is 2 SDs above.
- Kira, because 30 cm above the mean is more than Zee's 20 cm.
62 in a game with mean 50, SD 8. Luz: 41 in a game with mean 30, SD 4. Ari compares scores in two different games. Whose score stands higher compared with its own game's mean and SD?
- Jun, because the SD of 8 is larger than 4, so Jun has more room above the mean.
- Luz: 41 is 2.75 SDs above its mean, while Jun's 62 is 1.5 SDs above.
- Jun, because 12 points above the mean is more than Luz's 11.
- Jun, because 62 is higher than 41, so Jun's score stands higher in the game.
Tala
3.2 m on a team with mean 2.6 m, SD 0.2 m. Noah: 2.1 m on a team with mean 1.8 m, SD 0.1 m.
Bo compares long jumps on two different teams. Whose jump stands higher compared with its own team's mean and SD?
- Tala, because 3.2 m is longer than 2.1 m.
- Tala, because 0.6 m above the mean is more than Noah's 0.3 m.
- They are equal: each jump is 3 SDs above its team's mean.
- Tala, because the SD of 0.2 is larger than 0.1.
