From the
Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997
Histograms Worksheet
Datasets and Stories for Histograms
There is benefit in students using the same datasets for different analyses. It is efficient, as students don’t need to acquaint themselves with a new story for each display. If they are using a graphing calculator the students don’t need to enter a new set of data into the lists. (I recommend you read the article by Al Coons, Efficient Storing of Data on the TI-83, about storing data in a program for later use.) Another benefit is the opportunity to contrast the features of the data highlighted by each display. For these reasons I suggest the students use the datasets and stories on the stemplots worksheet when learning about histograms as well as the data generated when the students played Greed!.
Other datasets that are appropriate for histograms include Air Pollution, Bradmanesque, Oscar Winners, Speed of Light and Wild Horses. Follow the links to the datasets and from there to their stories.
Give students a set of data and the accompanying story. Students should realise that a dataset doesn't have a single histogram but many histograms, one for each choice of bin width. For 'nice' data, i.e. data that is symmetric and with no clustering or outliers, the set of histograms may all give the same general picture so the choice of histogram is not critical. With data that isn't so nice, different choices of bin widths may give histograms that look markedly different. For such datasets students will need to produce a variety of histograms, and then make and defend their choice as to which is 'best'.
Note that graphical calculators and computer statistics programs don't necessarily choose the best display by default and hence it is an unwise student who doesn't construct a few histograms of varying bin widths as part of their analysis.
After the histogram is drawn, students should
· locate the approximate centre of the distribution by eye;
· determine the spread of the data, and look for potential outliers;
· note the overall shape of the distribution;
· look for any other features of interest such as clustering or gaps.
Students need to practice writing a short report on the interesting features brought out by a graphical display. One approach would be to give each small group a different dataset and story and have them produce the display (say on a graphical calculator), discuss within the group the characteristics of the data brought out by the display, and then report to the class.
Using Technology
As noted elsewhere, it is quite time-consuming to draw a histogram, especially to match the quality and accuracy of a histogram drawn by even the simplest computer statistics program. Drawing a single histogram by hand should be sufficient for the students to get a feel for the mechanics of drawing a histogram, so additional histograms should be constructed using a computer or a graphical calculator. Let the technology shine in its sphere (repetitive algorithmic processes) and let the students shine in their sphere (looking for patterns, and deciding what the data say).
These remarks apply equally to other graphical displays, of course. It follows that students shouldn’t be required to construct any of these displays by hand for assessment purposes - it is a trivial exercise, and possibly the least important task you could ask a student to do in statistics.