1. AP STATISTICS Section 2.1: Measures of Relative Standing and Density Curves

3. Why do we use z-scores? 1. To express all observations on a common scale. 2. To compare relative standing of individuals on different scales. Ex. Test Scores Converting from a z-scores to a percentile depends on the shape of the distribution. Percentiles (again)

5. A mathematical model is a curve that best represents the distribution of the data. Why do we use mathematical models? Gives a compact picture of the distribution. Ignores minor irregularities. Ignores outliers. Easier to work with. A density curve is a curve that lies on or above the x-axis and has an area of 1 underneath it.

6. ***The area under the curve represents the proportion of observations that fall over a given range on the x-axis. Ex. 1. Density Curves a. Find the height so that the curve is a density curve. b. Find the proportion of observations that fall over the given range of X:

7. Median of a density curve is the point on the x-axis in which we have equal areas. Mean of a density curve is the balance point on the x-axis (ignoring the curve). Since density curves represent the distribution of the population, we will use μ for the mean and σ for standard deviation.

8. Ex. 2. a. Confirm that this is a density curve b. Find the proportion of observations that fall over the given range of X: X < 0.25 X > 0.60 X = 0.60 X < 0.60 0.32 < X < 0.80