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Understanding Normal Distributions & Empirical Rule in Statistics

Learn how to analyze normally distributed data using the empirical rule (68-95-99.7 rule) in statistics. Understand properties of normal distribution, create frequency tables, find mean, median, and mode. Master the concepts of standard deviation, symmetric distribution, and the bell curve.

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Understanding Normal Distributions & Empirical Rule in Statistics

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  1. Given the following data 82, 94, 81, 93, 80, 100, 97, 102, 80, 80, 81 Find the mean, median, and the mode. Sketch a box and whisker plot Create a frequency table with width size of 5 starting at 80 -84. Then find the angles to represent each width.

  2. Normal Distributions and the Empirical Rule OBJECTIVE: Use the empirical rule (68-95-97 rule) to analyze data Page 11

  3. Data that is normally distributed ACT or SAT Scores Height IQ scores Biological measures

  4. Normal Distribution Normal Distribution is a type of frequency distribution graph. The graph of a Normal Distribution is called a statistic distribution curve or more commonly referred to as a bell curve..

  5. Properties of the Normal Distribution • Mean, median, & mode are the same • The data is symmetric aboutthe mean • Area under the curve equals1 or 100%. • Curve never goes below the x-axs • Standard deviation σ controls the spread of the curve.

  6. Limits to the mean and standard deviation • The mean ranges between 1 and infinity • The standard deviation must be positive

  7. The Empirical rule (68-95-99.7 rule) In the normal dist. with mean μ and standard deviation σ. • 50% of the observations fall below the mean. • 50% of the observations fall above the mean.

  8. The Empirical rule (68-95-99.7 rule) In the normal dist. with mean μ and standard deviation σ. • 68% of the observations fall within of the mean. • 95% of the observations fall within of the mean. • 99.7% of the observations fall within of the mean. 1σ 2σ 3σ

  9. Behold the normal curve 68% 34% 34% 0.15% 95% 0.15% 13.5% 13.5% 2.35% 2.35% 99.7%

  10. Let’s Practice (p. 12)

  11. Classwork & Homework Classwork – get with your project partner and decide on a topic for your project and a time to complete the survey. Homework – page 13 in your packet

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