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A Stem and. . . Flower Show Kc>j*uwrds: Teaching: Examination Question: Diagrammatic Representation:

H um ou r .

At Paisley College of Technology, I teach a one-year Statistics course to first-year students for the BSc degree in Land Economics. The course is continually assessed and I try to provide a blend of problem-type exercises and report-type courseworks.

As part of the final coursework, one of the questions was of the type Comriicwt brief(!, on rod1 of'(lic.,fhllo~~,ing statrments: One of the statements was A stom rrriri Icwf' diagruni is u s d to orguniir tlic cli.splu!..v ut u f i o ~ . c ~ r .vlion~.

What follows is a selection of replies. Some have been edited but they d o show the range of replies possible.

1. A stem and leaf diagram is a way of displaying data and serves the wine purpose as any other form of diagram. e.g., pie chart, cartesian chart. or bar graph, i.e.. i t may show the different flowers. etc. in the tlower show but is not an implement for organizing the displays at a flower show.

2. Rubbish!!! A stem and leaf display has nothing t o d o with flower shows apart from the fact that the person who first thought of the stein and leaf must have had a really vivid imagination and have been obsessed with horticulture. Either that o r he couldn't think of anything sensible to call the graphical inethod of presenting data which he had just discovered.

3. A stem and leaf display could be used to organize at a flower show, by showing the amount of space or some other factor that each display was to have. However. a stein and leaf display is in fact a pictorial method of statistical display which can aid presentation and comprehension of a statistical report, by illustrating figures i n ;i clearer and more informative way than say the standard bar chart.

4 . Somebody does have a creative mind! No. seriously, a stein and leaf diagram (.sic,) is used to display a large group of statistics in a primarily visual way. I t is quite conceivable that such ii system could be devised t o deal with horticultural problems.

5. No. A stein and leaf diagram is a method of graphing statistics and could be used in relation to statistics for the flower show but has much wider uses.

6 . This statement at first may seem to be a bit of a joke, but on further analysis i t seeins that i t most certainly is a joke. I don't think a stem and leaf diagram would aid the organization of the displays at a flower show unless i t were used to calculate what plants people looked at most. (Highly unlikely.)

7. A stem and leaf diagram is used to display mathematical data and so i t could not possibly be used t o organize at a flower show.

8 . Good joke. But I suppose i t could be used but I think a plan would be better.

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9. In certain circles this may well be true, however, a stem and leaf display as we know it is used to display statistical data in an easily-to-interpret fashion-it shows the actual data and the frequency of occurrences grouped together in a tidy diagram.

IO. At last years pre-show committee meeting, it was decided that the layout of this years show would be different. Great controversy occurred when Chairman Willie Peapod suggested splitting Paisley Town Hall up into 3 sections; one for kiddies, one for old folks, and one for us, the middle aged. Willie is, in actual fact, 67!

He proposed that each stall at this years show would take a full census of each visitor toestablish theagegroups which areattracted to each stall and so. in order to be accurate and make sure no misunderstanding a rose, Willie proposed the use of a stem and leaf diagram. Well! there was uprage; Mrs Honeysuckle said that nobody was cutting up her lovely herbs to make a stupid diagram and while agreeing; Roddy Dendron said, it was all a waste of time.-(The herb pun.)

But Willie, forceful as ever, ploughed on regardless explaining that a stem and leaf diagram was nothing to d o with cutting up herbs or plants or anything like that. He described the different categories in the stem, grouping ages in tens and each person then be put in his or her group with the second number (the units number) as the leaf therefore showing the total numbers of people in each group but also the spread within the groups and any bias.

The result was very successful. At this years show all the bedding plants were in with the shrubs, all the veg. was with the herbs and all the lawnmowers were together with the greenhouses; all in all the Paisley Flower Show was a great success.

-Next week:- How Pie charts are used by bakers. I / . Gimmie a break!

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12. This statement is most definately (sic) T R U E as it is obvious that a stem and leaf diagram could only be used at a flower show, as much as a pie chart is used to display annual bakery turnovers, a population pyramid is used to assess population distribution figures in Egypt and a bar chart is used to show how many pints can be drunk before collapsing in a heap under the counter.

I S . I suppose this is a joke, if so I find it hilarious, if not I havent the foggiest idea.

14. This statement is correct. See Chris Anthemums Guide to Competitive Flower Arrangement published by C Rapp & Co 1987.

15. I suppose considering its the end of the year you would put in a trick question that might fool someone or maybe it was your idea of a joke.

Just because a flower has a stem and leaf doesnt mean that i t could be used for arranging a flower display. Ive honestly never heard so much rubbish. However, having said that. there will be some poor student that falls for it. A stem and leaf diagram is a way of displaying data, not flowers. It serves the same purpose as a pie chart o r a bar graph.

16. It is the consensus of opinion that some end-of-term wit is called for, not that stats is anything to laugh about-anyway please turn over.

Three Cheers for Pythagoras - _.. - ~- ... .

ALAN SYKES

Kc-,w.ordc: Teaching: Estimate of Variance; Regression, Linear: [-Test.

Two important considerations involved in teaching any discipline are:

(i) to demonstrate the connections between allied disciplines; ( i i ) to be in sympathy with long term objectives of the discipline.

In Tc.aching Stutistics (January 1984), Anna Hart suggests that i t is difficult to justify why we estimate a2 (and hence a) using squares of deviations. May I suggest one possible approach which also illustrates the above principles?

Unknowingly students facing this problem are investigating a simple example o f a LINEAR STATISTICAL MODEL. Subsequently in their A-level course they will meet the techniques oftwo-sample t and linear regression without realising that such topics are intimately connected. Only in the second year of a :,!atistics course at