Statistics: standard deviation comparison: formal vs range/6

Following up from the previous post, the tutor tries out the standard deviation estimator range/6.  Standard deviation is a common topic during high school math tutoring.

Imagine the following results from a fictional midterm:

56, 42, 71, 66, 45, 81, 75, 59, 62, 49, 68, 79, 58, 91, 63

First, we’ll arrange the marks in order:

42, 45, 49, 56, 58, 59, 62, 63, 66, 68, 71, 75, 79, 81, 91

Now, we’ll calculate the standard deviation using the formula (actually, using the Sharp EL-520W:)

σ=13.7 (sx), σ=13.2 (σx)

Now, using range/6:

range=91-42=49

σ=range/6=49/6=8.2

We see that, for a small sample anyway, the estimate range/6 is not necessarily close to σ.

Source:

Zimmer, Cooke, et. al. Mathematics of Data Management. Toronto: Nelson, 2003.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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