Chapter 2: Describing Location In a Distribution Section 2.1 Measures of Relative Standing And Density Curves

Case Study Read page 113 in your textbook

Where are we headed? Analyzed a set of observations graphically and numerically Consider individual observations

Consider this data set: How good is this score relative to the others?

Measuring Relative Standing: z-scores Standardizing: converting scores from the original values to standard deviation units

Measuring Relative Standing: z-scores A z-score tells us how many standard deviations away from the mean the original observation falls, and in which direction.

Practice: Let’s Do p. 118 #1

Measuring Relative Standing: Percentiles Norman got a 72 on the test. Only 2 of the 25 test scores in the class are at or below his. His percentile is 2/25 = 0.08, or 8%. So he scores in the 8 th percentile

Density Curves Histogram of the scores of all 947 seventh-grade students in Gary, Indiana. The histogram is: Symmetric Both tails fall off smoothly from a single center peak There are no large gaps There are no obvious outliers Mathematical Model For the Distribution

Density Curves

Density Curves: Normal Curve This curve is an example of a NORMAL CURVE. More to come later….

Describing Density Curves Our measure of center and spread apply to density curves as well as to actual sets of observations.

Proportions in a Density Curve

Describing Density Curves MEDIAN OF A DENSITY CURVE: –The “equal-areas point” –The point with half the area under the curve to its left and the remaining half of the area to its right

Describing Density Curves MEAN OF A DENSITY CURVE: –The “balance point” –The point at which the curve would balance if made of solid material

Mean of a Density Curve

Notation Use English letters for statistics –Measures on a data set –x = mean –s = standard deviation Use Greek letters for parameters –Measures on an idealized distribution –µ = mean –σ = standard deviation Usually