2.1 Describing Location in a Distribution

Percentiles The pth percentile of a distribution is the value with p percent of the observations less than it.

Percentiles The following stem and leaf plot represents the scores in Mr. Pryor’s statistics class. Jenny scored an 86. How did she perform on this test relative to her classmates.

Percentiles Determine the Percentiles Norman who scored a 72 Katie who earned a 93 The two students who earned scores of 80

Percentiles NOTE: Some people define the pth percentile of a distribution as the value with p percent of observations Less than or equal to, however we are sticking strictly to less than.

Percentiles The stem plot below shows the number of wins for each of the 30 major league teams in 2012. The Minnesota Twins (66 wins) Washington Nationals (98 wins) Rangers and Orioles (93 wins)

Frequency Tables Frequency Table- Displays the counts (frequencies) of a category Relative Frequency- Divide the counts from the frequency table by the total number of values and multiply by 100- to get a percent

Frequency tables Cumulative Frequency Table- Add the counts in the frequency column for the current class and all classes with smaller values Relative Cumulative Frequency- Divide the entries in the cumulative frequency column by the total number and multiply by 100 to convert to a percent

Age of US Presidents at inauguration Make a Relative Frequency Cumulative Frequency Relative Cumulative Frequency

Age of US Presidents at inauguration Frequency Relative Frequency Cumulative Frequency Relative Cumulative Frequency 40-44 2 45-49 7 50-54 13 55-59 12 60-64 65-69 3

Relative Cumulative Frequency Frequency Table Median Frequency Relative Frequency Cumulative Frequency Relative Cumulative Frequency 35 to <40 1 40 to <45 10 45 to <50 14 50 to <55 12 55 to <60 5 60 to <65 6 65 to <70 3

Cumulative frequency graph Plot the point corresponding to the cumulative relative frequency in each class at the smallest value of the next class These are sometimes also known as ogives

Inauguration ages of US Presidents

Inauguration ages of US Presidents Was Barack Obama, who was first inaugurated at the age of 47 unusually young? Estimate and interpret the 65th percentile of the distribution

Percentiles and quartiles Q1- roughly 25% of the data or the 25th percentile Q2 roughly 50% Q3 roughly 75% of the data or the 75th percentile

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Standardizing We can describe Jenny’s location in the distribution of her class’s scores by telling how many standard deviations above or below the mean.

Z-score A score tells how many standard deviations a value is from the mean. Observations larger than the mean have positive z scores. Observations smaller than the mean will have negative z-scores

Z-scores Use the information from Mr. Pryor’s statistics class to determine the z-scores for Jenny, who scored 86 Kate, who scored 93 Norman, who scored 72

Z-scores

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