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Delete - Last Modified By: BJO at 17/02/2015 9:59:49 AM
Think of how you might display the set of data generated by measuring the height, to the nearest centimetre (so we are talking about discrete, numerical data), of all of the students in your current Further Math class. How could we display this? We could use several methods, but here we will use a ‘stem and leaf’ display. What will this give us?
The data could be as follows (taken from BJO’s class of 2014):
Heights in cm = { 170, 178, 175, 173, 173, 175, 178, 160, 160, 163, 159, 163, 181, 161, 159, 160, 163, 160, 184, 182, 164, 157 }.
We need to split each value into parts for the ‘stem’ and parts for the ‘leaves’. It would be sensible to use the hundreds and tens values for the stem and the units for the leaves. Thus, in the data set above, the stem values could be { 15, 16, 17, 18 } and the leaf values (in this case) are the numbers { 0, 1, 2, 3, 4, 5, 7, 8, 9 }.
The Stem runs down the page and the leaves run across the page as follows:
S|
T| l e a f
E|
M|
Key T|l = (some data value)
Note the use of a separator character – the vertical line ‘|’ to show where the stem values stop and where the leaf values start. Note also the use of a ‘Key’, which is an explanation of how the data is displayed – it is a very necessary part of the diagram (don’t forget to draw it, particularly in the exams!). The height data from above could now be drawn as:
15| 7 9 9
16| 0 0 0 0 1 3 3 3 4
17| 0 3 3 5 5 8 8
18| 1 2 4
Key 17|5 = 175cm
More things to note: the stem values increase down the page. The leaf values are rank-ordered into increasing values from left to right. The leaf values are repeated if there is more than one height with the same value (e.g. there are four values of 160cm in the above diagram).
Stem plots are a useful way to represent univariate data, particularly when there are a small number of values (say less than thirty). Unfortunately, your CAS calculator cannot do Stem plots!