# Understanding Data Distribution and Analysis in AP Statistics

Explore the concepts of percentiles, standard scores, and data transformation in AP Statistics. Learn to interpret data distributions, calculate percentiles, and examine the relationship between percentiles and quartiles. Engage in activities to analyze class heights, calculate z-scores, and understand the impact of unit conversions on statistical measures. Dive into ogives and cumulative frequency graphs to gain insights into data representation techniques in statistics.

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## Presentation Transcript

**Data Locations**AP Statistics September 08, 2016**Goals**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.**Activity**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.)**Activity**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.)**Activity**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?**Percentiles**Definition: The percentage of observations less than a specific data point.**Finding Percentile**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.**Percentiles**What is the relationship between percentiles and quartiles?**Ogives**Cumulative relative frequency graphs.**Ogives**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.)**Ogives**Find their cumulative relative frequency. Create an ogive (cumulative relative frequency graph). Extra time? Work on homework!