Drawing and comparing Box and Whisker diagrams (Box plots)

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Presentation transcript:

Drawing and comparing Box and Whisker diagrams (Box plots) Interpreting data … Drawing and comparing Box and Whisker diagrams (Box plots)

Learning objectives Calculate quartiles and draw box and whisker diagrams Interpret box and whisker diagrams and use to compare datasets Use all terminology and use IQR to find “outliers”

A list of data The weights (KG) of 15 children: 37, 42, 31, 35, 48, 29, 50, 36, 44, 28, 63, 35, 41, 52, 43 Difficult to UNDERSTAND what these children look like from the list …

Another useful summary A diagram to show: min (28KG), max (63KG), median (41KG) … Min Median Max

Median ½(n + 1)th piece of data (ordered) 28, 29, 31, 35, 35, 36, 37, 41, 42, 43, 44, 48, 50, 52, 63 15 items of data … n = 15 ½(n + 1) = ½(15 + 1) = 8th item

Lower Quartile ¼(n + 1)th piece of data (ordered) 28, 29, 31, 35, 35, 36, 37, 41, 42, 43, 44, 48, 50, 52, 63 15 items of data … n = 15 ¼(n + 1) = ¼(15 + 1) = 4th item

Upper Quartile ¾(n + 1)th piece of data (ordered) 28, 29, 31, 35, 35, 36, 37, 41, 42, 43, 44, 48, 50, 52, 63 15 items of data … n = 15 ¾(n + 1) = ¾(15 + 1) = 12th item

Add that to our box plot Median LQ UQ Max Min A diagram to show: min (28KG), lower quartile = 35KG max (63KG), upper quartile = 48KG median (41KG) … Median LQ UQ Min Max

Some terminology Q2 Q1 Q3 Q0 Q4 Median LQ UQ Min Max Alternative names for quartiles

Some terminology UQ – LQ = Interquartile Range (IQR) Max – Min = Range

Some terminology Positive skew: median closer to LQ than UQ Negative skew: median closer to UQ than LQ Symmetrical distribution

Interpreting the box plot Easily see lightest / heaviest and range The ‘box’ contains the middle 50% of people (the most ‘representative half’) The ‘whiskers’ show the lightest 25% and heaviest 25% of people (extremes)