Lesson 24 Data relations

# Data relations

Overview Resources
An activity on relational and combined data. Pupils collect data on the number of girls in their own and their parents’ households when they were at a similar age. They discuss how to see if the proportion of girls runs in the family, and in the end see that this is a correlation issue, and select an appropriate way to process the information. Data collection completed at home before the lesson- see below
Correlation and probability
• Examine critically the mathematical presentation of information,
• Linking probability of events to probability of combined events.
• Preparation
Ask pupils to find the number of females under the age of 16 and the total number of people in their mother's (or main carer's) household when she was their age, and to record this information along with the same data for their current household. Explain that the data will be used to check the hypothesis that ‘Having more girls than boys aged less than 16 in a household (or vice versa) runs across generations: They should bring the information in on an un-named slip of paper. They should also record the same data for their father’s family.
EPISODE 1
First round of organising data
Data on paper slips are collected and displayed in ratio terms on the board under two headings, with the class considering variations and possible links as it unfolds. They are then asked in pairs and groups to think how to analyse the data. The sharing of ideas then helps to clarify the hypotheses the data was collected to confirm or disconfirm, leading to more advanced work in the next episode.
EPISODE 2
Comparing data on two variables through a correlation grid
By classifying data according to two variables, e.g. more girls in current/more girls in mother’s versus more girls in current/fewer girls in mother’s and so on, pupils construct 2 by 2 and 3 by 3 relational tables and check for confirming and disconfirming cases. They would discuss issues of degrees of likelihood, possible causation (e.g. every ‘mother’s family’ includes at least one girl) and sample size. An extension is possible, organising the data as a full scatter.
Notes on household data collection
All real-life social data are complex and sometimes sensitive. This complexity, which is partly due to definition of words, can be made a point for useful social and personal discussion before or after the mathematical activity. Here we emphasise that a household is composed of people who currently and normally live in the same flat or place, and mother can mean the main adult female who takes the main caring role in that household. If there is no such adult female, then the male carer can provide his data, when he was the same age as the pupil is now. It is very unlikely that the hypothesis as formulated holds in general, but local variations can emerge because of the sample size, which then becomes a point of discussion. In all cases pupils should benefit from considering real social data, however complex, as much as from the exploration of correlation and use of relational data.