1 / 28

Section 9.3 Transformations of Data

Section 9.3 Transformations of Data. Objectives: 1. To find z-scores and other transformed scores for data. 2. To determine the effect of transformations on the mean and standard deviation. Original . Transformed. 4 6 7 9 9 10. 9 11 12 14 14 15. Mean 7.5

russellcoleman
Télécharger la présentation

Section 9.3 Transformations of Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 9.3 Transformations of Data

  2. Objectives: 1. To find z-scores and other transformed scores for data. 2. To determine the effect of transformations on the mean and standard deviation.

  3. Original Transformed 4 6 7 9 9 10 9 11 12 14 14 15 Mean7.5 St Dev2.26 12.5 2.26

  4. Theorem 9.1: Translated Data Let x1, x2, . . ., xnrepresent the original data. If y1, y2, . . ., ynare obtained by adding a constant k to the original data values, then y = x + k and sy = sx.

  5. Original Transformed 4 6 7 9 9 10 12 18 21 27 27 30 Mean7.5 St Dev2.26 22.5 6.77

  6. If y1, y2, . . ., ynare found from x1, x2, . . ., xn by multiplying each by the same constant k, then y =kx and sy = ksx. Theorem 9.2: Scaled Data

  7. x - x z = s Definition z-score The transformed score found by subtracting the mean from the individual score, and dividing by the standard deviation:

  8. The statistic z is a measure of the deviation of an individual score from the mean in units of standard deviation.

  9. x - x 135 - 100 = z = 16 s Practice: If you scored a 135 on an IQ test that has a mean of 100 and standard deviation of 16, how many standard deviations are you away from the mean? ≈2.2

  10. A z-score of 2.2 on the IQ test means that the score earned (135) was 2.2 standard deviations (16) above the mean (100). If the individual score x is the same as the mean, the z-score is 0. A score below the mean will result in a negative z-score.

  11. Practice: Use the given set of scores to find the following values. 63, 74, 67, 76, 77, 71, 68, 66 Find the mean.

  12. Practice: Use the given set of scores to find the following values. 63, 74, 67, 76, 77, 71, 68, 66 Find the standard deviation.

  13. Practice: Use the given set of scores to find the following values. 63, 74, 67, 76, 77, 71, 68, 66 Find the z-score of the lowest score.

  14. Practice: Use the given set of scores to find the following values. 63, 74, 67, 76, 77, 71, 68, 66 Find the z-score of the highest score.

  15. Practice: Use the given set of scores to find the following values. 63, 74, 67, 76, 77, 71, 68, 66 Transform the rest of the scores to z-scores.

  16. Homework: pp. 460-461

  17. If the mean is 83 and the standard deviation is 7, find the z-score for each test score below. 1. 88

  18. If the mean is 83 and the standard deviation is 7, find the z-score for each test score below. 5. 73

  19. If the mean of a set of data values is 75 and the standard deviation is 10, find the mean and standard deviation for the data transformed as follows. 9. y = 1/5x - 10

  20. SAT scores are calculated from z-scores using the transformation SAT = 100z+500. 16. Give the mean score on the SAT.

  21. SAT scores are calculated from z-scores using the transformation SAT = 100z+500. 17. Give the standard deviation on the SAT.

  22. SAT scores are calculated from z-scores using the transformation SAT = 100z+500. 18. Give the SAT score of someone who scored 2.5 standard deviations above the mean.

  23. SAT scores are calculated from z-scores using the transformation SAT = 100z+500. 19. What does an SAT score of 563 mean?

  24. ■ Cumulative Review 26. A line passes through (3, 4) with an angle of inclination of 20°. Write its equation in slope- intercept form.

  25. ■ Cumulative Review 27. State the three Pythagorean identities.

  26. ■ Cumulative Review 28. In class, three quiz scores range from 10 to 20 with a median of 18. Find the mean, midrange, and mode.

  27. ■ Cumulative Review 29. Graph r = 2 + 3 cos .

  28. ■ Cumulative Review 30. If sin  = , give the other five trig functions in terms of a and b. a b

More Related