# Why is my 8th grade Algebra 1 tutoring student learning mean absolute deviation and standard deviation?

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.

• Also I’m not sure why $x_i-\mu$ wasn’t squared in the formula they used for variance… Jan 13 at 2:45
• 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. Jan 13 at 4:39
• 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. Jan 13 at 8:14
• 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.) Jan 13 at 9:33
• 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. Jan 13 at 9:41