Lesson 30 How do I handle the data?

# Episode 2

Reasoning Resources:
Worksheets 1, 2 and 3, Graph paper
Small group work on two sets of data
The groups make a choice, and process each of the three data sets.

Further metacognition should result when they compare and contrast each other's solutions in whole class discussion at the end.
Suggest that different groups start with different data sets, but each should finish at least two. It may be an advantage if you yourself have no prior preference for method, so you are prepared to be persuaded by more than one method. Even if two or more groups choose the same method for a data set, the details are likely to be different.

Groups should present their solutions on large paper or OHT for display during subsequent discussion.

Class discussion on flexibility of modes of analysis of data
Visual comparison of two sets of data, each of which represented by tally marks for bar charts, may be best done as a stem-and-leaf, which is no more than two charts placed back to back. Categories and scale must be the same.

Graphical representation allows comparisons and estimated intermediate values.

Both correlation and comparisons of representative values such as mode, mean and median are useful in many cases.
Get groups to present their solutions for each data set separately. They can then
summarise which method worked best and why other methods were not helpful. Some of the ideas expressed briefly in the first discussion will be visited again, now with greater insights from pupils

Encourage comparisons between the two sets of data, to emphasise aspects such as the following: In the GCSE results all data are individual: there are two unrelated separate groups to be compared by grades. So each grade (or top two grades, or bottom two grades, and so on) can be a base for comparison, as well as the overall picture of a bar chart or tally chart. The ideal way would be two stem-and-leaf diagrams set back to back, as used in TM5: Sam and the newspaper. But a bar chart of Grades A to u with the girls' and boys’ numbers put alongside each other will do. But first they need to tally the data so as to count the numbers getting each grade.

The English/science KS3 levels can be explored along the lines of the correlation lessons pupils have covered, leading to scatter graphs. On the other hand some representative values such as mean, median or mode may be usefully explored too, because of the ordinal numeric sets of ordered pairs (E,S) for the two groups. But they would not now be looking for a functional relationship, as in the second problem, but comparing the two correlational ones. When they do this they will see that the assertion is true - however they choose to look at it, the spread of boys’ results is wider than that of the girls.In the science experiment, there are two types of relationship: the relationship between the same temperatures and values for time, and the similarity between the two tables due to the fact that the entries in one are about twice the other. Graphical representation may be helpful to estimate times for middle value temperatures and to show the pattern, but bar charts are also feasible, even though they do not allow intermediate results. The relationship with temperature is an exponential one and they will see two parallel curves, with one going twice as fast as the other at all temperatures. So the relation with amount of chemical A is a linear one, They may also spot that in both cases, for every 10° temperature rise, the speed approximately doubles.
Extension
The extension questions below give an opportunity for some classes to re-run the two-step metacognitive process in other contexts. Someone claims that people's height and hand-spans go together. What data would you collect to check this, and how would you process it? You want to choose between two holiday resorts, Ilfrapool and Blackcombe. You want to be sure of getting a lot of sun for the last week in July. You find records for each town of the number of hours of sun that week in each of the resorts over the fast 20 years. At first glance you can see that Blackcombe varies between 35 and 53 hours, whereas Iifrapool can be as low as 23 and as high as 70 hours.
End of Lesson Reflection
Pupils can step back to describe the two steps in their work on each Activity. First there was a brainstorm and sharing of intuitions, then detailed work and modification to methods. In all cases two sets of data were compared, but different contexts required different modes of representation.