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Standard Deviation

Standard Deviation. 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. Normal Distribution.

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Standard Deviation

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  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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