Standard deviation

Grade 9 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Luz tested two phone batteries 8 times each, in hours. Both sets have mean 20. Which set has the larger standard deviation (SD)?

   • Set A, because its value 27 is the farthest from 20, so A is more spread out.
   • Set A, because its range of 8 is bigger than B's range of 6, so A is more spread out.
   • Neither, because both sets have the same mean of 20, so their spreads must match too.
   • Set B: most of its values sit 3 hours from 20; A's mostly sit 1 hour away.
2. 2.

   Noah timed two bus routes 6 times each, in minutes. Both sets have mean 40. Which set has the larger SD?

   • Neither, because both sets have the same mean of 40, so their spreads must match too.
   • Neither, because both sets have the same range of 12, so their spreads must be equal.
   • Set A, because its value 50 is the farthest from 40, so A is more spread out.
   • Set B: its values are typically farther from 40 than A's are.
3. 3.

   Esme measured two plant groups after 6 weeks, in cm. The means are 60 and 80. Which set has the larger SD?

   • Set A, because its range of 12 is bigger than B's range of 10, so A is more spread out.
   • They cannot be compared, because the two means are different from each other.
   • Set A, because its value 70 is the farthest from its mean, so A is more spread out.
   • Set B: all its values sit 5 from its mean; A's mostly sit 2 from its mean.
4. 4.

   Ren logs minutes late for two buses. Bus A: mean 8, SD 1.5. Bus B: mean 8, SD 4. Which reading is correct?

   • Every ride on Bus B is exactly 4 minutes away from the mean of 8 minutes.
   • Only the spread differs: Bus A's lateness stays closer to 8 minutes than Bus B's.
   • Bus B is usually later than Bus A, because its SD is larger than A's SD.
   • Bus A is late 1.5 minutes on average and Bus B is late 4 minutes on average.
5. 5.

   Kira measured 30 sunflowers: mean 140 cm, SD 12 cm. Which reading of the SD is correct?

   • The tallest and shortest sunflowers in the group differ by 12 cm from each other.
   • A typical sunflower, not every one, is about 12 cm taller or shorter than 140 cm.
   • Every sunflower in the group is exactly 128 cm or exactly 152 cm tall.
   • The average sunflower in this group is 12 cm tall, and 140 cm is its spread.
6. 6.

   Tala's quiz scores have mean 82 and SD 5. Which reading of the SD is correct?

   • Every quiz score is exactly 77 points or exactly 87 points.
   • The best and worst quiz scores differ by 5 points from each other.
   • A typical quiz score, not every one, is about 5 points above or below 82.
   • The average quiz score is 5 points, and 82 is how spread out the scores are.

7. Read this first

   Use this

   Table. Pages: 9, 11, 12, 13, 15. Gap from 12: -3, -1, 0, 1, 3. Squared gap: 9, 1, 0, 1, 9.

8. 7.

   Zee read for 5 days. Pages: 9, 11, 12, 13, 15, with mean 12. The table shows each squared gap. What is the SD of these 5 days?

   • 4
   • 2
   • 20
   • 6

9. Use this

   Table. Minutes: 24, 28, 30, 32, 36. Gap from 30: -6, -2, 0, 2, 6. Squared gap: 36, 4, 0, 4, 36.

10. 8.

    Bo practiced drums for 5 days. Minutes: 24, 28, 30, 32, 36, with mean 30. The table shows each squared gap. What is the SD?

    • 80
    • 16
    • 12
    • 4

11. Use this

    Table. Height: 11, 17, 20, 23, 29. Gap from 20: -9, -3, 0, 3, 9. Squared gap: 81, 9, 0, 9, 81.

12. 9.

    Jun flew a kite on 5 days. Height in meters: 11, 17, 20, 23, 29, with mean 20. The table shows each squared gap. What is the SD?

    • 18
    • 36
    • 180
    • 6
13. 10.

    Table. Apples: 12, 14, 16, 18. Gap from 15: -3, -1, 1, 3. Squared gap: 9, 1, 1, 9. Ari counted apples on 4 trees: 12, 14, 16, 18, with mean 15. The table shows each squared gap. What is the SD, to the nearest tenth?

    • 5
    • 6
    • 20
    • 2.2