3. Finding the Percentile of a Data Value Percentile (position) of a specified data value, x = a. Percentiles: The following data is the number of chocolate chips in 40 randomly selected Chips Ahoy cookies. Find the percentile ranking for a cookie with 23 chocolate chips. + 19 19 20 20 20 20 22 22 22 22 23 23 23 23 23 23 23 24 24 24 24 24 25 25 25 25 25 25 25 26 26 26 26 26 26 27 27 28 28 30 Interpret this percentile: b. Percentiles: I fellow faculty who played in last year's World Series of Poker in Las Vegas. Out of 4425 entrants in the Senior No-Limit Hold-em Championship, she finished in 147th place (from the top). What is her percentile rank? Interpret this percentile. 4. Quartiles The median cuts the data into 2 equal parts. Quartiles cut the data into 4 equal parts. Q2 is the same as the Q1 is Q3 is lowest 25% of data -> Q1 Q2 Q3->highest 25% of data a. Speeding. A group of BYU-Idaho students collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 25 mph. The recorded speed of 14 randomly selected vehicles is given below: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40 Find and interpret the quartiles for speed in the construction zone. Q = _ Q2= Q3 = _i 5. Interquartile Range lowest 25% of data- ->Q1 Q2 Q3-->highest 25% of data The Interquartile Range, IQR is the length of the It is computed as the difference between the first and third quartile: 6. Using the IQR to check for Outliers What does it mean to be an "outlier"? An the data. % of the data. is an unusually high or unusually low data value compared to the rest of a. What are the Upper and Lower Fendce formulas? Upper Fence: Lower Fence: If any data value is considered an outlier. -or- b. Find the Outlier. If a 15th car came through the construction zone at 100 mph: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40, 100 then it is IQR = Upper Fence: Lower Fence: 7. 5-Number Summary Use the 5-number summary: MIN-Q1----M -Q3-------MAX The three quartiles plus the min and max for the original Speeding problem above. min = Q1 Q2 (median)= Q3= I