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# Class Opener – Day 35 – Tall and Short

We’re thinking about standard deviation in my 9th grade class, and the idea of variation and “unusual” data points. I think the picture which greeted students today says just about all which needs to be said on standard deviation, doesn’t it?

Later in class, I asked students to plot their heights on a number line I had drawn, with a low of 60 inches and a high of 74.  From here, I asked students to estimate what our class standard deviation might be.  Some interesting responses were generated:

• 10 – probably because 60 and 70 appeard on the line.
• 5 – because that would seem to cover the number line

When I reminded them that standard deviation can be thought of as “typical distance from the mean”, the responses evolved and eventually we settled on between 2 and 3, where travelling 2 standard deviations in each direction would cover everyone in the class.  Next, when I told them that the World’s Tallest Man had a height over 8 standard deviations from the mean, meaningful gasps were shared, and we could move on to notes onvolving the normal distribution.

Short post today as I am about to start 23 parent conferences over 6 hours….wish me luck!

## By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

## 5 replies on “Class Opener – Day 35 – Tall and Short”

“When I reminded them that standard deviation can be thought of as typical distance from the mean,…”
This “thought of” looks more like the mean absolute deviation from the mean. Standard deviation is the square root of the average of the squares of the deviations about the mean, not the same thing.

the phrase “typical distance” actually comes from rubrics from the AP Stats exam, of which I am a grader. The term “typical” is not intended to convey an exact measure, like a mean distance, but instead provides communication of the meaning of the computed statistic.

For reference, see problem 1 from the 2007 exam, and the associated rubric.

A question : Do they do anything with variance in this course?

Much is done with variance, as we can only combine random variables by using the variance.