1 / 9

The Empirical Rule

The Empirical Rule. Standard Deviation and the Normally Distributed Data Set. Normal Distribution. Data Values 5 6 7 8 9 10 11. S -3 -2 -1 0 1 2 3. x. Data values 2 4 6 8 10 12 14.

astin
Download Presentation

The Empirical Rule

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Empirical Rule Standard Deviation and the Normally Distributed Data Set

  2. Normal Distribution Data Values 5 6 7 8 9 10 11 S -3 -2 -1 0 1 2 3 x Data values 2 4 6 8 10 12 14

  3. The Empirical Rule • When • The standard deviation is known • The mean is known • & the data is normally distributed (like a bell-shaped mound) • Then • The Empirical Rule can be used to generalize some properties about the distribution (data) • Also known as the sigma rule; 68-95-99.7 rule

  4. Normal Distribution Percent of values under portions of the normal curve 34.13% 34.13% 13.59% 13.59% 2.14% 2.14% 0.13% 0.13% S -3 -2 -1 0 1 2 3 x

  5. The Empirical Rule • When data is normally distributed: • Approx. 68% of the values will fall within +/- 1 S from the x 68% S -3 -2 -1 0 1 2 3

  6. The Empirical Rule • When data is normally distributed: • Approx. 95% of the values will fall within +/- 2 S from the x 95% S -3 -2 -1 0 1 2 3

  7. The Empirical Rule • When data is normally distributed: • Approx. 99% of the values will fall within +/- 3 S from the x 99.7% S -3 -2 -1 0 1 2 3

  8. Approximate Empirical Calculations • Approximate Calculations • 68% = x +/- 1(s) • [ x – 1(s), x + 1(s)] • 95% = x +/- 2(S) • [ x – 2(s), x + 2(s)] • 99% = x +/- 3(S) • [ x – 3(s), x + 3(s)]

  9. SAT Distribution m = 490 and s = 100

More Related