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I’m tutoring an 8th grade student in Algebra 1, and he showed me that their class learned how to find standard deviation and mean absolute deviation using the following formulas:

$SD=\sqrt{\displaystyle\frac{\Sigma (x_i-\mu)^2}{n}}$

$\textbf{Mean Absolute Deviation}=\displaystyle\frac{\Sigma |x_i-\mu|}{n}$

I did not learn this when I was in Algebra 1 in 8th grade, and I was in the honors class. Is this because of Common Core? I know they’re trying to scatter more stats materials in the regular curriculum but I’m just shocked he was working on this at his level. He eventually understood it and was getting the correct answers but he definitely struggled a lot with it today before getting there. Just don’t understand why they’re covering this at this level — it seems a little advanced to me.

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    $\begingroup$ Also I’m not sure why $x_i-\mu$ wasn’t squared in the formula they used for variance… $\endgroup$
    – blakedylanmusic
    Jan 13 at 2:45
  • $\begingroup$ That was the formula on their sheet and it was typed out. To be fair, the expression was written there all by itself, without being set equal to "variance". It's possible it was supposed to be another parameter besides variance. It's beyond me why the teacher would include these formulas on the sheet and leave no indication as to what they represent. $\endgroup$
    – blakedylanmusic
    Jan 13 at 4:39
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    $\begingroup$ Your formula for variance is actually what is called Mean Absolute Deviation. It is a statistic for measuring data dispersal that is different than standard deviation but not intrinsically less valid. $\endgroup$
    – Matthew Daly
    Jan 13 at 8:14
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    $\begingroup$ Very basic concepts of descriptive statistics seem fine, but the use of subscripts and $\Sigma$-notation seems a bit over-the-top to me for students just learning how to do things like translate "three more than twice the sum of two numbers" to "$3 + 2(x+y)$ and solve equations like $2 - 3x = 5x.$ (And everyone at my school did this in 9th grade, but that was in the early-mid 1970s, and of course I and a handful of others never bothered to limit ourselves to what was done in class, in the same way that those interested in basketball did not limit themselves to what was done in P.E. class.) $\endgroup$
    – Dave L Renfro
    Jan 13 at 9:33
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    $\begingroup$ To clarify, by "did this" I'm referring to very basic algebra notions (up to trinomial and difference of squares factoring, and ending with the quadratic formula), and NOT to descriptive statistics. I don't think descriptive statistics was covered other than maybe calculating an average from a set of numbers (sometimes having to be read off of a bar graph), although I suspect standard deviation might have been mentioned in a supplementary "Extra for Experts" type section. $\endgroup$
    – Dave L Renfro
    Jan 13 at 9:41

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Short answer: Yes, the Common Core (correctly, IMO) believes that workers in the twenty-first century should have an elementary grounding in some topics of what you probably believe to be college-level statistics.

Longer answer: Every state is free to interpret and implement the standards as they wish. This is especially true at the high school level, where the standards are broken down by topic instead of by grade level.

For instance, in New York, I don't believe students are ever directly exposed to the formula for variance and standard deviation. But students in Algebra 2 are asked to calculate p-values and the usual confidence intervals for normal distributions using graphing calculators. In Algebra I, by contrast, students need to be able to perform linear regressions and calculate correlation (again with a calculator) and be able to interpret bivariate data given a chart.

If I were to criticize what your student is being asked to do, it isn't because of difficulty so much as authenticity. Statistical analysis is something students should be well-practiced at, but they will be using tools like spreadsheets or statistical software to perform the calculations. But either your state feels differently or your student's teacher feels like taking the time to supplement the standards to involve grunt work. In the end, it's not a hill I would fight for on either side.

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    $\begingroup$ To be fair, she is only asking them to compute these values for 5-6 data points on the test. I'm not willing to necessarily die on a hill saying students shouldn't learn this in Algebra 1, but I do wonder if what they are being asked to do is a little beyond their capability at that stage of their mathematical development. Perhaps at that stage using software is better like you're saying. $\endgroup$
    – blakedylanmusic
    Jan 13 at 8:19
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    $\begingroup$ I am in agreement that statistics needs to be weaved into the curriculum. $\endgroup$
    – blakedylanmusic
    Jan 13 at 8:25

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