Learn By Doing – Standard Deviation

Published: December 21st, 2012

Category: Activity 1: Learn By Doing

The concept of standard deviation is less intuitive as a measure of spread than the range or the IQR. The following activity is designed to help you develop a better intuition for the standard deviation.

Background

At the end of a statistics course, the 27 students in the class were asked to rate the instructor on a number scale of 1 to 9 (1 being “very poor,” and 9 being “best instructor I’ve ever had”). The following table provides three hypothetical rating data:

A table of results showing that in class 1, one student rated the instructor a 1, one student rated the instructor a 9 and 22 student rated the instructor a 5. In class 2, 12 students rated the instructor a 1, 12 students rated the instructor a 9 and 1 student rating the instructor a 5. In class 3, each rating from 1 to 9 was chosen by exactly 2 students.

And here are the histograms of the data:

A graph of class 1, one student rated the instructor a 1, one student rated the instructor a 9 and 22 student rated the instructor a 5.

A graph of class 2, 12 students rated the instructor a 1, 12 students rated the instructor a 9 and 1 student rating the instructor a 5.

A graph of class 3, each rating from 1 to 9 was chosen by exactly 2 students.

Reveal the true standard deviations.


This document is linked from Measures of Spread.