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Box Plot: Measures of Position The quartiles help us identify the position of data. We saw earlier that each quartile represents 25% of the data. Therefore, Q1 is the 25th percentile, Q2 is the 50th percentile, Q3 is the 75th percentile, and the highest data value is the 100th percentile. You may be asking yourself, what is a percentile? If we think about percentages, we know that it takes 100 percent to make a whole, so each percent is a percentile mark. Percentiles may make more sense if we use an example. Think about standardized testing. You may have been told that you scored in the 80th percentile. It does not mean that you made an 80 on the test. It means that you scored better than 80% of the students who took the same standardized test. So why do we use quartiles in box plots instead of percentiles? Can you imagine what a graph would look like if we used vertical lines to mark all of the percentiles? We would have 101 lines (the smallest data value plus 100 percentiles), which would be pretty hard to read. Quartiles are a way of breaking up the graph so the we can easily estimate the percentile location of a raw data value. Consider the graph below. What percentile do you estimate 64 to be? High Temperature, March 12 - 21, 2017 68 Temperature (F) Sixty-four is between the first and second quartile so it is between th and th percentile. We can estimate 64 to be at the 35 + rd/th percentile. Check