The London 2012 Olympic Games took place in July and August. During two weeks of competition a total of 117 Olympic records were broken, some by only hundredths of a second. Having superfast reaction times helps athletes to start and finish first.
Aussies kids’ reaction times were collected as part of the 2012 CensusAtSchool questionnaire. Students did an activity to test how quickly they could react with their hands: their dominant hand, and their non-dominant hand. Your dominant hand is the one you like to write with.
The mean (average) reaction time for all students who completed the activity was calculated for each year level. Why not check out data for your year level in the National Summary Tables?
The graph below – called a scatter plot – shows the mean (average) hand reaction time for boys using their preferred hand. Can you see the pattern in the data? As year level increases, reaction time decreases. As boys get older, their hand reaction time appears to get quicker.
The data in this graph slopes down, from left to right. This is called a negative relationship. There are many examples of negative relationships, such as amount of sleep and reaction time.
When the relationship between two variables is positive, the pattern in the graph would go up from left to right. A graph of height against belly button height would have a positive slope. As a child’s height increases, their belly button height also increases. What other positive relationships can you think of?
Going back to the graph of reaction times, you might assume that someone who left school in Year 12 last year has an even faster reaction time this year. To predict reaction times beyond Year 12, or reaction times for age groups that aren’t included in the original data, a line of best fit is drawn.
Statisticians have various techniques for finding such curves such as ‘best fit’ and ‘least squares’. By identifying the structure in the data, the bumps (errors) associated with the measurements are smoothed out (are removed from consideration). Finding such lines or curves is fundamental in assisting statisticians and mathematicians in increasing understanding about the data and making useful predictions.