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Understanding Normal Distribution and Standard Deviation for High School Students

Learn about Normal Distribution, Standard Deviation, and IQ Scores through interactive examples and calculations to enhance statistics knowledge and interpretation skills. Explore the bell curve concept and how data is represented and analyzed.

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Understanding Normal Distribution and Standard Deviation for High School Students

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Presentation Transcript

  1. Standard Deviation

  2. Focus 6 Learning Goal – (HS.S-ID.A.1, HS.S-ID.A.2, HS.S-ID.A.3, HS.S-ID.B.5) = Students will summarize, represent and interpret data on a single count or measurement variable.

  3. Normal Distribution • There are many cases where data tends to be around a central value with no bias left or right. This is called a Normal Distribution. • The “Bell Curve” is a Normal Distribution. • It is often called a “bell curve” because it looks like a bell. • The Normal Distribution has mean = median = mode.

  4. Standard Deviation • The standard deviation is a measure of how spread out numbers are. • Generally, this is what we find out: 99.7% of values are within 3 standard deviations of the mean. 95% of values are within 2 standard deviations of the mean. 68% of values are within 1 standard deviation of the mean.

  5. Learn more about Normal Distribution and Standard Deviations • The video to play as at the bottom of the screen.

  6. Refresher on 1, 2 and 3 standard deviations from the mean.

  7. IQ Scores • An IQ score is the score you get on an intelligence test. The scores follow a normal distribution. • What percent of people have an IQ score between 85 and 115? • What percent of people have an IQ score between 70and 85? • What percent of people have an IQ score above 130? • In a population of 300 people, how many people would you expect to have an IQ score above 130? 68% 13.5% 2.5% 0.025(300) = 7.5, 7 or 8 people in a group of 300 would have an IQ score greater than 130.

  8. Standard Deviation • Example: 95% of students at school are between 1.1 m and 1.7 m tall. Assuming the data is normally distributed, calculate the mean and standard deviation. • The mean is halfway between 1.1m and 1.7m. • Mean = (1.1 + 1.7)/2 = 1.4 m • 95% is two standard deviations either side of the mean (a total of 4 standard deviations) so: • 1 standard deviation = (1.7 – 1.1)/4 • = 0.6/4 • = 0.15 m Mean Each interval is 0.15 below or above the mean. Multiply 0.15 by 2 then 3 to get the 2nd and 3rd intervals.

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