Mean absolute deviation

[lilaclorax]

Two questions in reference to 6.SP.5.c

If the standard says IQR and/or Mean Absolute Deviation- do students need to be able to do both or would they be able to answer any question using just one?

Two- What are the benefits of using Mean Absolute Deviation rather than IQR? In other words, what is the payoff in 6th graders learning Mean Absolute Deviation?

[pstinchcombe]

Mathematically, I think the mean absolute deviation is more sensitive to outliers — and it makes sense for a measure of spread to be sensitive to outliers. For example, the IQR of the data set {4,5,6,6,7,8,9} is the same as the IQR of {1,5,5,8,8,8,20} — the quartiles are 5 and 8 — but I think any reasonable person would say the second set is more dispersed.

From a practical standpoint, I think IQR is rarely used by professionals, so students are unlikely to see it reported. If part of the goal of S&P curriculum is to prepare students to understand stats they encounter, IQR does very little to serve that goal. MAD isn’t very often used either (I think it is used more commonly than IQR, but it’s still not very standard), but it’s closer to the measure of spread which actually is used most often, which is standard deviation.

[pstinchcombe]

On question two:

Mathematically, I think the mean absolute deviation is more sensitive to outliers — and it makes sense for a measure of spread to be sensitive to outliers. For example, the IQR of the data set {4,5,6,6,7,8,9} is the same as the IQR of {1,5,5,8,8,8,20} — the quartiles are 5 and 8 — but I think any reasonable person would say the second set is more dispersed.

From a practical standpoint, I think IQR is rarely used by professionals, so students are unlikely to see it reported. If part of the goal of S&P curriculum is to prepare students to understand stats they encounter, IQR does very little to serve that goal. MAD isn’t very often used either (I think it is used more commonly than IQR, but it’s still not very standard), but it’s closer to the measure of spread which actually is used most often, which is standard deviation.

[Bill McCallum]

The Mean Absolute Deviation is intended as a more intuitive precursor concept to the Standard Deviation. It makes sense to take the mean of all the absolute deviations if you want to get a quantitative measurement for the spread; it turns out for rather subtle reasons that taking the square root of the sum of the squares of the deviations (that’s what the Standard Deviation is) is better, but you can’t really explain the reasons at this level, and the more complicated procedure might obscure the underlying idea.

[TR]

Please comment on the practical application of MAD or IQR. I need to re-teach every thing my daughter is taught in school. By the way, I did not delve into statistics until college. Why the push for a 6th grader to learn statistics?

thanks for any help

[Bill McCallum]

I certainly hope your 6th grader is not being exposed to statistics at a college level! Grade 6 statistics in the Common Core is meant to be an introduction to some basic ideas of data and variability. It is actually pretty important for people to have that ability these days, since we are presented with statistics all the time in newspapers, reports about polling, discussions of important issues like climate change and polling bias, and so on. Not to mention the pervasiveness of statistics in more specialized jobs in the scientific, technical, medical, and biological fields.

But really the purpose of this blog is not to have general discussions about the importance of learning mathematics and statistics, but rather to answer specific questions about the standards. So if you can point to specific standards that you have questions about, that you think your child’s curriculum might not be treating correctly, then I’d be happy to answer them.

It’s possible that the curriculum your child is experiencing is just spending too much time on this, so I’d be interested to know if you think that is the case.

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