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The top box is smaller and the whiskers do not extend as far.ĭrawing two boxplots above the same number line supposes that the data behind each deserve to be compared.
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The second thing to note about the two box and whisker graphs is that the top plot is not as spread out at the bottom one. The vertical line inside both of the boxes is at the same place on the number line. The first is that the medians of both sets of data are identical. There are a couple of features that deserve mention. Above a second boxplot has been drawn above the one that we have constructed. Two different data sets can thus be compared by examining their boxplots together. Give some advantages and disadvantages of Box plots over other methods of comparing data.Box and whisker graphs display the five-number summary of a set of data.
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When do we feel our ‘extreme’ data is just TOO extreme?Ģ6 Outliers High Outliers > UQ + 1.5 x IQRĢ7 Plenary What’s the point in Box plots? Which scores (if any) might be considered ‘outliers’ and why (/why not)?Ģ3 boys and 11 girls were given a maths test. Non-smokers smokers Direct comparisons easy with box plotsĢ2 23 boys and 11 girls were given a maths test. The Queue of DEATH! 25,000 people 25,000 people 25,000 people 25,000 people Source: Dr Pearl’s 1938 study of 100,000 smokersĢ0 Direct comparisons easy with box plots The Queue of DEATH! 25,000 people 25,000 people 25,000 people 25,000 people Source: Dr Pearl’s 1938 study of 100,000 non smokers
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“Heaviest boy same as heaviest girl” “All of the most representative half of girls lighter than most representative half of boys” “Three quarters of girls lighter than three quarters of boys” “Heaviest boy heavier than heaviest girl” “Most representative half of girls generally lighter than most representative half of boys”ġ7 Comparing groups Boys Girls “Lightest girl same as lightest boy” Negative skew: median closer to UQ than LQ Symmetrical distributionĮasily 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)ġ6 Comparing groups Boys Girls “Lightest girl lighter than lightest boy” Minimum = 28KG Maximum = 63KG Range = 35KG Mode = 35KG Median = 41KG Mean = 40.9KG Slightly easier to understand with these summary figures …ĥ Stem and leaf … 28, 29, 31, 35, 35, 36, 37, 41, 42, 43, 44, 48, 50, 52, Key: 2 9 means 29 ORDERED STEM & LEAF We now have the raw data AND a pictorial representation …Ī diagram to show: min (28KG), max (63KG), median (41KG) … Min Median MaxĨ Median ½(n + 1)th piece of data (ordered)Ģ8, 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 itemĩ Lower Quartile ¼(n + 1)th piece of data (ordered)Ģ8, 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 itemġ0 Upper Quartile ¾(n + 1)th piece of data (ordered)Ģ8, 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 itemġ1 Add that to our box plot Median LQ UQ Max MinĪ diagram to show: min (28KG), lower quartile = 35KG max (63KG), upper quartile = 48KG median (41KG) … Median LQ UQ Min Maxġ2 Some terminology Q2 Q1 Q3 Q0 Q4 Median LQ UQ Min Maxġ3 Some terminology UQ – LQ = Interquartile Range (IQR) Max – Min = Rangeġ4 Some terminology Positive skew: median closer to LQ than UQ Interpreting data … Drawing and comparing Box and Whisker diagrams (Box plots)Ĭalculate quartiles and draw box and whisker diagrams Most: Interpret box and whisker diagrams and use to compare datasets Some: Use all terminology and use IQR to find “outliers”ģ 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 …Ĥ The weights (KG) of 15 children: 28, 29, 31, 35, 35, 36, 37, 41, 42, 43, 44, 48, 50, 52, 63 Presentation on theme: "Drawing and comparing Box and Whisker diagrams (Box plots)"- Presentation transcript:ġ Drawing and comparing Box and Whisker diagrams (Box plots)