### 9.3 Describing Dispersion

• Math Help

In the histogram in Example 3, "SD" stands for standard deviation. This notation will be used in graphs in the rest of this chapter.

Here are some observations about normal distributions and the normal distribution graph on page 426 (also shown below).

• Because the graph is symmetrical about the mean, you can draw a vertical line through the mean and both halves are mirror images.
• 50% of the data lies below the mean and 50% of the data lies above the mean.
• The mean, median, and mode are equal.
• Data values that are farther than 2 standard deviations from the mean are considered unusual. Notice that 4.6% of the data values are farther than 2 standard deviations from the mean.
• Data values that are farther than 3 standard deviations from the mean are considered very unusual. Notice that 0.2% of the data values are farther than 3 standard deviations from the mean. • Consumer Suggestion

The National Council for Teachers of Mathematics provides a histogram tool that contains data sets of interesting examples. You can also enter your own data and create a histogram. To access the tool, visit NCTM Illuminations.

• Checkpoint Solution

The number of chest sizes within 2 standard deviations of the mean is

185 + 420 + 749 + 1073 + 1079 + 934 + 658 + 370 + 92 = 5560.

This is or about 96.8% of the total. This is close to the 95.4% predicted by a normal distribution.

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