Warm-Up If the variance of a set of data is 12.4, what is the standard deviation? If the standard deviation of a set of data is 5.7, what is the variance?

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Presentation transcript:

Warm-Up If the variance of a set of data is 12.4, what is the standard deviation? If the standard deviation of a set of data is 5.7, what is the variance? If the mean of a set of data is 12.7 and the standard deviation is 1.74, what range should you consider to look for outliers? If the lower quartile of a data set is 32.3 and the IQR is 6.7, what range should you consider to look for outliers?

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Vocabulary Normal Distribution – A data distribution where the data form a bell curve that has distinct statistical properties. Z-Score – the number of standard deviations from the mean. Used to tabulate the area under a normal curve.

Essential Question and Standards How do we determine quartiles and percentages for standardized tests?

Normal Distribution The distributions of most continuous random variables will follow the shape of the normal curve. The mean, median, and mode all exist at the center of the curve.

Formula

The Empirical Rule Defined by the number of standard deviations data is from the mean. 68% of data within 1σ 95% of data within 2σ 99.7% of data within 3σ

Finding a Range of Data

Example 1 Given a mean of 45 and a standard deviation of 6 The middle 68% of data should fall in the range: The middle 95% of data should fall in the range: The middle 99.7% of data should fall in the range:

Example 2 Given a mean of 810 and a standard deviation of 57 The middle 68% of data should fall in the range: The middle 95% of data should fall in the range: The middle 99.7% of data should fall in the range:

Example 3 Given a mean of 20.5 and a standard deviation of 3.75 The middle 68% of data should fall in the range: The middle 95% of data should fall in the range: The middle 99.7% of data should fall in the range:

Example 4 Given the data below, calculate the range for the middle 68% of the data, the middle 95% of the data, and the middle 99.7% of the data. 77, 29, 53, 54, 27, 61, 87, 35

Example 5 Given the data below, calculate the range for the middle 68% of the data, the middle 95% of the data, and the middle 99.7% of the data. Does this data seem to be normally distributed? 46, 57, 48, 59, 18, 37, 73, 32

Example 6 Find the range of possible means and estimate a standard deviation.

Example 7

Example 7 (cont’d) b) What percent of women are taller than 69.5 inches? c) Between what heights do the middle 95% of women fall? d) What percent of women are shorter than 62 inches?