![]() ![]() We can see that the swimmer seems to swim at speeds consistently within 4 seconds of 56 seconds, with a personal best time of 50 seconds. Teachers can highlight how the plots organise the data to make this information accessible.Īs students become familiar with the plots and with statistical thinking, they should be encouraged to attend to range, outliers, distribution, mean, median, and so on.įor example the plot below is from data for a swimmer’s times for 50m freestyle. Mode and range and the general shape of the distribution are easiest to see. Their descriptions will become increasingly sophisticated, as they see more features in the plots. After students make a plot, they should describe what the plot shows about the data. Students need opportunities to practice the mechanics of producing dot plots and stem-and-leaf plots from data sets. They should also have the opportunity to use these representations and others in statistical investigations where they collect data for a purpose, analyse it and write a report on the findings.Īctivity 1: Describe it encourages students to interpret the data that they are plotting.Īctivity 2: Selecting stems gives students practice making appropriate choices for stem-and-leaf plots.Īctivity 3: Making comparisons advocates using real relevant data for producing data plots that allow comparisons. Students should use real and relevant data, should discuss the choices for producing good representations (features of these plots as well as specific choice of scale) and interpret the data in terms of the real situation from which it arose. Students should be given opportunities to produce both types of plots, but beyond initial demonstrations, such tasks should not be mere mechanical exercises. It is less obvious that 43 is the mode for this data set. The plot below shows that there are more values in the 40-44 range than any other region. The stem-and-leaf plot will reveal the modal region. For example, in the following dot plot it is obvious that the mode is 24. This does, however, depend on the chosen scale or stem values. It should be noted that most students will find it easy to choose multiples of ten as stems (or multiples of 100).Ī good user of these plots can make more sophisticated stem choices such as the range of 5 shown in the example on the right above (which has stems for 40-44, 45-49, 50-54, 55-59, etc.).īoth dot plots and stem-and-leaf plots produce representations that are related to bar graphs or histograms, and readily show the more frequent data. Both these features are more evident in the representation on the right.ĭata set For example, the two stem-and-leaf plots below depict the same data, but in the one on the left it is not obvious that there is an outlier (72 – not near other values), nor is the bi-modal (two-peaked) nature of the data revealed. Students may make inappropriate choices of stems for stem-and-leaf plots, resulting in too many data values being associated with each stem, or in a stem being omitted because there are no data values associated with it. Good stem-and-leaf plots require good choices of stems. Using 5mm grid paper helps with the spacing issue for this and for many other mathematical processes.Įxamples of bad plots: Box plots and stem-and-leaf plots only give a good pictorial representation of frequency when the 'dots' or 'leaves' are aligned. Using a word processor may not solve these problems because different numerals can have different widths. Careless plotting can result in misleading plots such as those shown below. Students appreciate that they have to take care when producing dot plots and stem-and-leaf plots because the success of the representation relies on evenly spacing the numbers or symbols. same scale, appropriately aligned, possibly back-to-back).įor more information see also: more about dot plots and stem-and-leaf plots. They then also make meaningful comparisons of 2 data sets by producing plots that can easily be compared (e.g. At this level, they can use the resulting plots to informally discuss the distribution of the data, including the range and the mode.Īt the next level, this discussion becomes more sophisticated and they identify the other measures of centre (i.e. Success depends on students being able to produce a dot plot or stem-and-leaf plot from a given data set, making appropriate choices of scale and/or stems. ![]()
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