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Transforming Data

Learn how to transform data through addition, multiplication, and z-scores to analyze distribution shapes, center, and spread for better insights. Understand density curves, uniform distribution, and calculating probabilities in statistics.

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Transforming Data

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  1. Transforming Data

  2. Let’s look at our test data!

  3. Transforming Data • Transforming converts the original observations from the original units of measurements to another scale. • Transformations can affect the shape, center, and spread of a distribution.

  4. What effect does adding have on the data?

  5. Effect of Adding (or Subtracting) a Constant • Adding the same number a (either positive, zeros, or negative) to each observation • Adds a to measures of center & position(mean, median, percentiles, but • Does not change the shape of the distribution or measures of spread (range, IQR, standard deviation).

  6. What if I multiplied everything by 10? Original Data

  7. Effect of Multiplying (or Dividing) by a Constant) • Multiplying (or dividing) each observation by the same number b (positive, negative, or zero). • Multiplies measures of center and location 9mean, median, quartiles, percentiles) by b • Multiplies measures of spread (range, IQR, Standard deviation) by |b|, but • Does not change the shape of the distribution.

  8. So… our last test scores. Change to a z-score:

  9. Original data has a mean of 50 and standard deviation of 5…. • What happens to both if we add 20 to each item? • What happen to both is we multiply 20 to each item?

  10. Density Curves

  11. Weight of newborns • Nearest pound • Nearest tenth of pound 4 5 6 7 8 9 4 5 6 7 8 9

  12. Fit more & more rectangles • It approaches a curve as the rectangles become smaller & has greater accuracy.

  13. Density Function • Describes the overall pattern of a distribution. • The area under the curve and above any interval of values on the horizontal axis is the proportion of all observations that fall in that interval. • The graph is a smooth curve called the density curve. • Total area under the curve = 1.

  14. Uniform Distribution • All occur in equal distributions

  15. Ex: What’s the area from 4.5 to 5.5? What’s the area from 5.5 to 6?

  16. If we have a uniform continuous function from 3 to 8, find the height.

  17. Ex. 0.02 • Find P(x < 10) • Find P(x < 35) 50 minutes

  18. Ex: 0.25 • Find P(x<4) • Find P(x<2)

  19. Ex: 0.02 50 100 • Find P(x<20) • Find P(x>70) • Find P(20<x<70)

  20. Homework • Page 107(19, 21, 23, 25) • Worksheet

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