## 30 August 2013

### Doing Statistics on Scientific Calculators, Grades 6-12

I'd be willing to bet that every approved syllabus on the College Board website for AP Statistics says that a graphing calculator (probably a TI, to be more specific) is required for success in the course. And while that probably IS true for AP Stats, that doesn't mean that all of the other kids doing statistics in your building need one!

Arguments Against Performing Statistical Calculations on Scientific Calculators
Whether you've said these things or know someone who has, I think its a prevalent attitude in schools because I've seen enough math teachers who cringe at the experience they had in college with statistics.

• "I barely ever get to stats in my curriculum, and when I do, my students just do mean/median/mode. It's a lot easier to just have them calculate that by hand, than teaching them how to use their individual model of calculator."
• "There's more value in having students perform these by hand so they can practice perseverance and have an understanding where the numbers come from."
• "If kids want to study statistics, they can do it in high school. We just do means and averages in my class."

Once Again, Common Core Changes Everything
As soon as the 6th grade, students are to be able to use descriptive measures like mean, median, and standard deviation to make decisions. Trust me when I say I don't really rely on a middle school student's ability to consistently compute a variance or standard deviation for a data set using the formula. You can make the process look simpler, but then you have a big chart on your paper, which also stresses kids out

Here are a few of the standards from 6th to high school: (from corestandards.org)
• CCSS.Math.Content.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:
• CCSS.Math.Content.6.SP.B.5a Reporting the number of observations.
• CCSS.Math.Content.6.SP.B.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
• CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
• CCSS.Math.Content.6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered
• CCSS.Math.Content.7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
• CCSS.Math.Content.HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
• CCSS.Math.Content.HSS-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
• CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
• CCSS.Math.Content.HSS-IC.B.6 Evaluate reports based on data.
• CCSS.Math.Content.HSS-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
How Are My Kids Going To Do All of This??
The good news: A built-in function to most every scientific calculator is the ability to enter a simple list and run a 1-variable stats analysis to get (at the very least) the distribution's count, mean, variance, and standard deviation.
More good news: According to Smarter Balanced's testing manual, students taking the high school tests will have access to statistical calculators on the test.
The bad news: The keystrokes are a bit different on every model, so teaching your students to use their scientific calculators to get measures of center or spread from a dataset will have to be more about principles of the process (entering the data into a list, finding the button/menu that has your mean/median/standard deviation in it), than it will be about walking through specific keystrokes with the whole class.

Tutorials To Share
You don't have to be an expert. Watch these yourself, share with your students on Edmodo or your class webpage and students can review the video relevant to their needs.

TI-30XS (Multiivew)

TI-30XA

TI-30X IIS

Casio fx-991ES

Casio fx-85ES

Casio fx-83MS

These are all the calculators I see MOST frequently in my lower level math classes. If you or your students have a different model, a simple Google or YouTube search with "statistics on [your model here] should at least get you started.