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 range of 8 is bigger than B's range of 6, so A is more spread out.
   • Set B: most of its values sit 3 hours from 20; A's mostly sit 1 hour away.
   • Set A, because its value 27 is the farthest from 20, so A is more spread out.
   • Neither, because both sets have the same mean of 20, so their spreads must match too.
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 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.
   • Neither, because both sets have the same mean of 40, so their spreads must match too.
   • Set B: its values are typically farther from 40 than A's are.
3. 3.

   Pia measured 5 sunflowers in each of two rows, in cm. Row B has the same pattern as Row A, just taller. Which row has the larger SD?

   • Row B, because its mean and values are larger, so its heights are more spread out.
   • Row B, because its biggest value, 88, is larger than any value in Row A.
   • They cannot be compared, because the two means are different from each other.
   • They are equal: each row's values sit the same distances from its own 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.
   • Bus A is late 1.5 minutes on average and Bus B is late 4 minutes on average.
   • Bus B is usually later than Bus A, because its SD is larger than A's SD.
   • Only the spread differs: Bus A's lateness stays closer to 8 minutes than Bus B's.
5. 5.

   Milo tracks points per game. Ari: mean 14, SD 2. Luz: mean 14, SD 6. Which reading is correct?

   • Luz scores more points per game than Ari, because an SD of 6 is larger than 2.
   • Only the spread differs: Ari's scores typically sit closer to 14 than Luz's do.
   • Luz scores exactly 8 points or exactly 20 points in every single game.
   • Ari scores 2 points a game on average and Luz scores 6 points a game on average.
6. 6.

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

   • The average quiz score is 5 points, and 82 is how spread out the scores are.
   • 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.
   • Every quiz score is exactly 77 points or exactly 87 points.

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?

   • 6
   • 4
   • 20
   • 2

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?

    • 12
    • 80
    • 16
    • 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?

    • 180
    • 18
    • 36
    • 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
    • 2.2
    • 20
    • 6