 By the end of this section, you should be able to: › Find and interpret the percentile of an individual value within a distribution of data. › Estimate percentiles and individual values using a cumulative relative frequency graph. › Find and interpret the standardized score (z- score) of an individual value within a distribution of data. › Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.

 Take the heights of each student (in inches) and place them on a number line from 58 inches to 78 inches.  Make a dot plot.  What percent of the students have a height less than yours? (This is percentile.)

 With a partner, find the mean and standard deviation of the class heights.  Is your height above or below the mean?  How many standard deviations is it from the mean? (This is your z-score.)

 What would happen if we converted the height to centimeters? (1 inch = 2.54 centimeters.)  How would the unit change affect measures of center, spread, and location (percentile and z-score) that you calculated?

 Definition: The percentage of observations less than a specific data point.

 Here are the scores of 12 exams taken in a class. The bold score is Jenny’s.  79, 81, 77, 74, 86, 90, 79, 93, 75, 80, 67, 72.  Find the percentile Jenny scored in.

 What is the relationship between percentiles and quartiles?

 Cumulative relative frequency graphs.

 Find the ages of everyone in the class and record their frequency. (How often they occur)  Find their relative frequency. (Number of occurrences / total)  Find their cumulative frequency. (Each frequency added to previous frequency.)

 Find their cumulative relative frequency.  Create an ogive (cumulative relative frequency graph).  Extra time? Work on homework!