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4.3 Quartiles, IQR and Box and Whisker Plots

4.3 Quartiles, IQR and Box and Whisker Plots. Quartiles….what?. Quartiles are really just the median or special medians. Definitions (on your sheet). Quartile- a median of an ordered set First Quartile/Lower Quartile- the median of the lower half of an ordered data set

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4.3 Quartiles, IQR and Box and Whisker Plots

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  1. 4.3 Quartiles, IQR and Box and Whisker Plots

  2. Quartiles….what? Quartiles are really just the median or special medians

  3. Definitions (on your sheet) Quartile- a median of an ordered set First Quartile/Lower Quartile- the median of the lower half of an ordered data set Second Quartile/Median- the median of an ordered set Third Quartile/Upper Quartile- the median of the upper half of an ordered data set Interquartile Range (IQR)- the difference between the upper quartile and the lower quartile of a data set.

  4. Example (on your sheet) Data Set: 4,3,6,5,2 Find the quartiles and the IQR. 2, 3, 4, 5, 6 1st Step : Put the terms in order 2nd Step : Find the median and draw line though it This divides the set into the lower half and upper half. 2, 3, 4, 5, 6 LowerHalf UpperHalf

  5. Lower (1st ) Quartile = 2.5 3rd Step: Find the median of the lower half – this is called the lower quartile or 1st quartile. 2, 3, 4, 5, 6 Since there is no middle term, do the average (2+3)/2= 2.5

  6. Upper (3rd) Quartile = 5.5 4th Step: Find the median of the upper half – this is called the upper quartile or 3rd quartile. Since there is no middle term, do the average (5+6)/2 = 5.5 2, 3, 4, 5, 6

  7. IQR- Interquartile Range = 3 Step 5 : Find the interquartile range (IQR) The IQR is the range between the upper and lower quartiles so just subtract. IQR = Upper Quartile – Lower Quartile 5.5 – 2.5 =??

  8. Box & Whisker Plots A way to represent the quartiles visually. Lower Quartile Upper Quartile Median of the data set Lowest number in set Highest number in set

  9. One last example…. Data Set: 8, 6, 3, 5, 3, 4, 2, 9 Find the quartiles, IQR and draw the box and whisker plot to represent the data and the quartiles……

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