Basic statistical measures, which students learn pretty early on, such as mean, median, mode, range and quartile, are very useful when comparing data and making decisions. However, statistics, without understanding these basic values, can be very deceiving. If there is a visual, without understanding the scale, or the context to the data, or knowing what a mean versus a median represents, it’s easy to be fooled into believing something that is actually untrue.
The warning here - don't trust statistics without understanding where the data comes from and what the data actually represents. Not something I think is done generally - just listen to the news or read the papers/magazines. Heck - look at our politicians and the 'false' or deceptive statistics (among other things) constantly quoted or visually shown. A lot of statistics (verbal and/or visual representations) come with none of the background data or context, so imagine how much deceit - intentional and unintentional - is occurring. (Always fun to check out the 'fact checks' of political speeches to realize the spin put on many statistics). There is a great article, (Why Not to Trust Statistics) with visuals that exemplifies potential 'deceit' by Ben Orlin - it's a great read and maybe something to share with students.
A major problem here is that many people do not understand the statistics. What's a mean? What's a range? What's a mode? What's a median? Lack of understanding, lack of data context, combined with a deliberate spin on the statistics, either verbally and/or visually, leads to confusion, misrepresentation, bad decisions, believing something to be true when it's not, and so much more. It's scary. And only with education can this "lack of understanding" or maybe it's better to say "willingness to believe what we see/hear" be combated.
This made me think about how we teach statistics - usually with a group of data points or just a list of numbers with little context, which students then calculate the statistical measures and graph the results. But do we spend enough time comparing these different measures ( I am just thinking about measures of central tendency here) or really work with outliers and how these impact the measures. Do we put enough context to these numbers so that the meaning of these measures truly makes sense? Do we provide context, real data, and real opportunities to look at visuals and verbal representations of statistics and make sense of them, in order to help students make informed decisions?
In the video below, I use data from a fictional company to show you how to use the fx-991CW to enter the data and calculate the 1-variable statistics. Then, with the QR capability, I show you a visual of that data and talk about histograms and box-and-whiskers and how the data can be misinterpreted if you don’t have the context.
Additional resources for basic 1- and 2- variable statistics and box-and-whisker.
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