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Published byValerie Wilson Modified over 9 years ago
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Standard Deviation Normal Distribution
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A common type of distribution where more values are closer to the mean, and as you move away from the mean, there are less data.
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Normal Distribution The more data collected the histogram will start to form a very distinct shape.
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The Bell Curve The distribution will be very bell shaped.
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The Bell Curve Very specific percentages of the area are located within one and two standard deviations of the mean.
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Percentages About 68% of the data will lie within one standard deviation from the mean. M ± SD (Likely that data will lie in this interval) About 95% of the data will lie within two standard deviations from the mean. M ± 2SD (Very likely that data will lie in this interval) Considered Not Likely that data will lie outside the 95%.
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Example 1 Suppose the number of songs on students iPods was recorded and the mean was 160 with a standard deviation of 35. 68% of the students should have songs between what values? 95% of the students should have songs between what values?
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Example 2 There are 240 smokers at PA. A sample was taken and the mean number of smokes per day was 12 with a standard deviation of 3. What percentage of students smoke between 6 and 18 smokes per day. Using the sample, how many students would you expect to smoke between 9 and 15 smokes per day?
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Significant Differences If a piece of data lies within 95% of the data we say that this is not a significant difference from the mean. If it lies outside the 95%, this is considered to be a significant difference.
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Significant Difference - Example Paula checks three samples of wheel bearings. The first is assumed to have a mean lifetime of 2000 h and a standard deviation of 400 h. The second and third boxes are unlabelled. She selects an item from each box The sample from box 2 fails after 1300 h. The sample from box 3 fails after 2900 h. Is either of the findings significant?
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Confidence Intervals We can accurately say that the population mean is within 95% of the sample mean.
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Confidence Intervals Example: Dana conducted a survey on how much money students typically spend per week on lunch. His sample of 40 randomly chosen students gave a mean of $15.25. Dana knows that the standard deviation is $2.00. What is the population mean.
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Confidence Intervals Example: $15.25 + 2($2.00) = $19.25 $15.25 – 2($2.00) = $11.25 Dana can be 95% confident that the population mean is between $11.25 and $19.25.
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