STANDARD DEVIATION

Mathematics

Previous Lesson

understand that the standard deviation is a measure of the spread of the data

realize the standard deviation is affected by outliers (extreme data points)

understand how the standard deviation and mean are affected when new data points are added

Objectives of Lesson

Standard Deviation for Ungrouped Data

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7

Standard Deviation for Grouped Data

Standard Deviation

Score 1 2 3 4 5 6 7

Frequency 1 2 3 4 3 2 1

Score 1 to 3 4 to 6 7 to 9

Frequency 6 9 1

The MeanThe mean of set of scores is the sum of the scores divided by the number of scores.

Along with the median and the mode, the mean is just one measure of the central tendency of a set of scores, but the mean is by far the most common and the most useful.

Mean

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7

The Standard Deviation

Although the mean tells us where the centre of a set of scores is, it does not tell us how widespread those scores are. 

For example: The scores 45, 55, 50, 53, and 47 have a mean of 50.  But the scores 20, 80, 50, 38, and 62 also have a mean of 50.  Note, however, that the second set of scores is much more variable (widespread) than the first set.  So in addition to a measure of central tendency, we need a measure of variability (spread of data).

The standard deviation (SD) is, roughly, the average amount by which the scores in a set differ from the mean. 

The scores in the first set above differ from the mean (50) by 5, 5, 0, 3, and 3.  So on average, they differ from the mean by a shade over 3.  The scores in the second set differ from the mean (again 50) by 30, 30, 0, 12, and 12. So on average, they differ from the mean by about 17. 

Standard Deviation

Learning Activity

Go to http://padlet.com/wall/SDactivity

2. Applet: http://www.math.usu.edu/~schneit/CTIS/SD/index.html

1. Use of Calculator to find mean and SD: www.padlet.com/wall/SDLesson

1. We use standard deviation to measure the spread of a set of data from its mean.

2. The higher the standard deviation, the more widespread is the set of data.

3. Standard deviation is useful to compare the spread of two sets of data which have approximately the same mean.

Standard Deviation

Next LessonComparison of Two Data Sets

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