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

2. 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”

3. 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 …

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

5. 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

6. 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

7. 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

8. 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

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

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

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

12. 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)