SWBAT: Use percentiles to locate individual values within distributions of data. Interpret a cumulative relative frequency graph. Find the standardized value (z-score) of an observation. Interpret z-scores in context. Do Now: The test scores for 14 AP Statistics students are given below. Find and interpret the standard deviation for this data.

SWBAT: Use percentiles to locate individual values within distributions of data. Interpret a cumulative relative frequency graph. Find the standardized value (z-score) of an observation. Interpret z-scores in context. Measuring Position: Percentiles Definition: The p th percentile of a distribution is the value with p percent of the observations less than it. Ex. Jenny earned a score of 86 on her test. How did she perform relative to the rest of the class?

SWBAT: Use percentiles to locate individual values within distributions of data. Interpret a cumulative relative frequency graph. Find the standardized value (z-score) of an observation. Interpret z-scores in context. Below is a frequency table that summarizes the ages of the first 44 U.S. presidents when they were inaugurated: Cumulative Relative Frequency Graphs Age of First 44 Presidents When They Were Inaugurated AgeFrequencyRelative frequency Cumulative frequency Cumulative relative frequency /44 = 4.5% 22/44 = 4.5% /44 = 15.9% 99/44 = 20.5% /44 = 29.5% 2222/44 = 50.0% /44 = 27.3% 3434/44 = 77.3% /44 = 15.9% 4141/44 = 93.2% /44 = 6.8% 4444/44 = 100%

SWBAT: Use percentiles to locate individual values within distributions of data. Interpret a cumulative relative frequency graph. Find the standardized value (z-score) of an observation. Interpret z-scores in context. (a) Was Barack Obama, who was inaugurated at age 47, unusually young? (b) Estimate and interpret the 65th percentile of the distribution. Interpreting Cumulative Relative Frequency Graphs

SWBAT: Use percentiles to locate individual values within distributions of data. Interpret a cumulative relative frequency graph. Find the standardized value (z-score) of an observation. Interpret z-scores in context. Measuring Position: z -Scores Definition: A z -score tells us how many standard deviations from the mean an observation falls, and in what direction. Ex. Jenny earned a score of 86 on her test. The class mean is 80 and the standard deviation is What is her standardized score?

SWBAT: Use percentiles to locate individual values within distributions of data. Interpret a cumulative relative frequency graph. Find the standardized value (z-score) of an observation. Interpret z-scores in context. Example: Jenny earned a score of 86 on her statistics test. The class mean was 80 and the standard deviation was She earned a score of 82 on her chemistry test. The chemistry scores had a fairly symmetric distribution with a mean 76 and standard deviation of 4. On which test did Jenny perform better relative to the rest of her class?