Lesson 2
1. Lesson 2
1.6. Explore 6
Module 4: Statistical Reasoning
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Standard deviation is also used as a measure of consistency. This tells us whether the process used to generate the data is consistent. When the standard deviation is low (i.e., the data is closely clustered around the mean), the process used to generate the data can be thought of as being more consistent than a process that generated data with a high standard deviation (i.e., the data is more spread out around the mean).
For example, a company that makes lids for coffee cups may take a sample of 100 lids and measure them. If the standard deviation is low—in other words, the lids are all very close to the same size—then the process used to make the lids is consistent. However, if the standard deviation is high—the size of the lids is very different—then the process used to make the lids is not consistent. It is certain that the stores that buy the lids want to know that the process to make the lids is consistent.
The calculation of standard deviation is an important part of summarizing and interpreting data.
Read “Example 1: Using standard deviation to compare sets of data” on pages 256 and 257 of your textbook. How can range and standard deviation be used by companies for quality control?
As you have been progressing through each lesson, you have been adding to your notes organizer. Remember to update your notes organizer with any new information you have learned in this lesson.
Add any new terms you come across to your Glossary Terms document. You can either add terms to your existing Glossary Terms document in your course folder or you can open a Glossary Terms document and start a new list for this module. You can also go to Mathematics Glossary to find more information, including examples, for the terms presented in this lesson.
At this point, you may find it helpful to refer to “In Summary” on page 260 of your textbook.