Standard deviation

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   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?

   • Class A's scores are more spread out, because its SD of 4 is smaller.
   • Both classes average 78, but Class B's scores are more spread out.
   • Class B did better, because its standard deviation is larger.
   • The classes did equally well, so their scores look alike.
2. 2.

   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 a larger SD means faster trips, so its trips will be shorter.
   • Route B: trips average 2 minutes longer but stay near 22, so it is rarely late.
   • Route A, because its larger SD means steadier trips that rarely run past 25 minutes.
   • Route A, because its mean time of 20 minutes is shorter than Route B's mean of 22.
3. 3.

   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 A is more consistent, even though Team B scores more on average.
   • Team B is more consistent, because a larger SD means better scores.
   • Team B is more consistent, because its mean of 17 is higher.
4. 4.

   Jun's water temperatures have an SD of 2.5 °C. Converting with F = 1.8 × C + 32, what is the SD in °F?

   • 2.5 °F
   • 4.5 °F
   • 8.1 °F
   • 36.5 °F
5. 5.

   Kira's race times have an SD of 1.5 minutes. Every time is multiplied by 60 to give seconds. What is the SD in seconds?

   • 61.5 seconds
   • 90 seconds
   • 1.5 seconds
   • 8,100 seconds
6. 6.

   Every plant grows exactly 2 cm taller. Before, the mean was 30 cm and the SD was 1.8 cm. Tala asks: what is the SD after?

   • 1.8 cm
   • 3.8 cm
   • 32 cm
   • 3.6 cm

7. 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.

8. 7.

   Zee compares scores on two different tests. Whose score stands higher compared with its own test's mean and SD?

   • Pia, because the SD of 7 is larger than 4, so Pia has more room above the mean.
   • They are equal, because each score is 14 points above its mean.
   • Bo: 84 is 3.5 SDs above its mean, while Pia's 94 is 2 SDs above.
   • Pia, because 94 is higher than 84, so Pia stands higher on a test.

9. 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.

10. 8.

    Luz compares sunflowers from two different rows. Which sunflower is taller compared with its own row's mean and SD?

    • 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.
    • Kira, because 150 cm is taller than 70 cm, so Kira's sunflower stands higher.
11. 9.

    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 62 is higher than 41, so Jun's score stands higher in the game.
    • Jun, because 12 points above the mean is more than Luz's 11.

12. 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.

13. 10.

    Bo compares long jumps on two different teams. Whose jump stands higher compared with its own team's mean and SD?

    • They are equal: each jump is 3 SDs above its team's mean.
    • Tala, because 3.2 m is longer than 2.1 m.
    • Tala, because the SD of 0.2 is larger than 0.1.
    • Tala, because 0.6 m above the mean is more than Noah's 0.3 m.