Catalyst notebook #3 Analyzing and Interpreting Exercise Data
#1 Write: Five Statements
a) The range of data (the gap between the biggest number and the smallest number) is 210 mins, which means there is a big variation of the measures. Possible reasons underlying it might be worth exploring.
b) The difference between mean and median is small, indicating that there are few odd numbers, if any, and the numbers are stable and scattered rather evenly.
c) Though without a benchmark, it can be told from the mean and median that students exercise for about 2.5 hours every week (20 mins every day on average), which should be an adequate time duration.
d) The durations of the exercising time that take up the three highest percentages are 180 mins, 150 mins and 210 mins, which are pretty close. Adding up the percentages, it can be identified that more than 50% of the students have a relatively long time of exercising per week.
e) The percentage for the shortest time (30 mins) and the longest time (240 mins) is close (13% vs. 12.5%), meaning that nearly 70 students exercise far too less and 70 students far too much compared with the average level.
#2 Consider and categorize: whether the arguments from different stakeholder are manipulative, objective, misleading, accurate and unfair.
Both the arguments from the principal and the parent were manipulative, misleading and unfair as they either focused on the peak number or minimum value while ignoring the bigger picture. In addition, no context was provided. For example, is this a regular week or a particular week? Maybe there was some field work for certain classes that would require going outside more often. Different conclusion can be drawn depending on which aspect of the data set we focus on and under what circumstances the data was produced.
In terms of categorizing my own statements, I would say statement a), b) and c) are objective as they just interpret the data per se without many judgements. Among these, statement a) might be manipulative as it pointed out the big range of the data and implicate further investigation. Statement d) and e) could be unfair as they both relied on a piece of the data set.
#3 Connect: Is communication about always correct, just because it is "good“ data?
I don't think so. As long as the data is produced, collected and interpreted by human, then it is biased and subjective in some way. For example, we cannot say the data that the principal and the parent referred to are bad or wrong data. However, based on their different hidden purposes and the conflict of interests, both of them only captured a piece of the big picture to amplify the effect of the point that they would want to make.
#4 Reflect: Is it possible for data to be technically accurate but still misleading? How? Why?
That's absolutely possible. One reason is that there could be different techniques to process the raw data and even for the same set of raw date there could be different statistical results depending on which tool we used and from what angle do we want to describe the data. Another reason is that every interpretation of the data should accompany context and there could be extra influencing factors that were not identified. For example, I exercise a lot and eat less, so technically speaking, the date regarding the gap of the calories that I create should make me lose weight. However, I didn't lose much weight. Then the hidden influencing factor was found - I got a low basal metabolic rate, probably due to my habit of skipping the breakfast. Therefore, relying only on a single source of data could be misleading, even though that data is technically accurate.

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