Transforming Data
Let’s look at our test data!
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.
What effect does adding have on the data?
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).
What if I multiplied everything by 10? Original Data
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.
So… our last test scores. Change to a z-score:
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?
Density Curves
Weight of newborns Nearest pound Nearest tenth of pound 4 5 6 7 8 9 4
Fit more & more rectangles It approaches a curve as the rectangles become smaller & has greater accuracy.
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.
Uniform Distribution All occur in equal distributions
Ex: What’s the area from 4.5 to 5.5? What’s the area from 5.5 to 6?
If we have a uniform continuous function from 3 to 8, find the height.
Ex. 0.02 50 minutes Find P(x < 10) Find P(x < 35)
Ex: 0.25 Find P(x<4) Find P(x<2)
Ex: 0.02 50 100 Find P(x<20) Find P(x>70) Find P(20<x<70)
Homework Page 107(19, 21, 23, 25) Worksheet