# Lesson 1.4 Quartiles, Percentiles, and Box Plots.

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Lesson 1.4 Quartiles, Percentiles, and Box Plots

Box and Whisker Plot: Percentile: Five-Number Summary: Definitions -Divides the data set into four regions -Lower, middle, and upper quartiles -Interquartile range: Upper - Lower The p th percentile is a value in the set such that p percent of the numbers are ≤ that value. -min x - Q 3 -Q 1 - max x -Q 2

Finding an Outlier Find the IQR (the inter-quartile range) Multiply 1.5 * IQR Add this result to the 3 rd Quartile  any number greater than this result is considered an outlier Subtract this result from the 1 st Quartile  any number less than this result is considered an outlier.

PlayerNumber of Hits Andrews35 Bocci21 Cappeletti44 Downs29 Rodriguez27 Harris18 Isaacs35 Jordan39 King37 Nu48 Posey13 Robisch17 Rossi32 Washington59 Wheeler15 Identifying Quartiles a.) List the data from least to greatest: 13, 15, 17, 18, 21, 27, 29,, 35, 35, 37, 39, 44, 48, 59 b.)Find the median of the data, c.) Look at the data less than 13, 15, 17,, 21, 27, 29 Find the median of this group Q2Q2 32 Q1Q1 18 d.) Look at the data greater than 35, 35, 37,, 44, 48, 59 Find the median of this group. Q3Q3 39 e.) Are there any outliers?59

13, 15, 17, 18, 21, 27, 29, 32, 35, 35,37, 39, 44, 48, 59 102030405060 Smallest value Outlier Q1Q1 Q 2 median Q3Q3 * Largest value

Put in order: Find the median of the data (Q 2 ) = Find the median of the first half (Q 1 )= Find the median of the second half (Q 3 )= What number is at the 88 th percentile? Find the percentile rank of 7? 73% 2, 5, 8, 6, 7, 5, 9, 3, 9, 4, 1 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 9 5 3 8 9

Smallest value biggest Value Q1Q1 Q 2 median Q3Q3 2468 10 0

Homework Page 34 6-15, 18-24