2.  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.

3.  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.)

4.  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.)

5.  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?

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

7.  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.

8.  What is the relationship between percentiles and quartiles?

9.  Cumulative relative frequency graphs.

10.  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.)

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