Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Statistics: Normal Distributions, 68-95-99.7 Rule Contemporary Math Josh Engwer TTU 04 August 2015 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 1 / 17 Increasing the Sample Size of a Data Set n = 25 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 2 / 17 Increasing the Sample Size of a Data Set n = 50 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 3 / 17 Increasing the Sample Size of a Data Set n = 100 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 4 / 17 Increasing the Sample Size of a Data Set n = 1000 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 5 / 17 Increasing the Sample Size of a Data Set n = 5000 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 6 / 17 Normal Distributions A normal distribution describes many real-life populations such as: Heights of people Lifespans of a certain model consumer electronic device Standardized exam scores NOTATION: µ ≡ Mean of Population NOTATION: σ ≡ Std. Dev. of Population Josh Engwer (TTU) (Greek letter ”mu”) (Greek letter ”sigma”) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 7 / 17 Normal Distributions (Properties) Proposition (Properties of a Normal Distribution) Mean = Median = Mode = µ Curve is bell-shaped & symmetric w.r.t its mean, µ The total area under the curve is 1 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 8 / 17 Varying σ Changes the Shape of a Normal Distribution µ = 10 σ=1 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 9 / 17 Varying σ Changes the Shape of a Normal Distribution µ = 10 σ=2 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 10 / 17 Varying σ Changes the Shape of a Normal Distribution µ = 10 σ=3 Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 11 / 17 68-95-99.7 Rule Given a normal distribution: Roughly 68% of the data values are within 1 standard deviation from the mean. Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 12 / 17 68-95-99.7 Rule Given a normal distribution: Roughly 95% of the data values are within 2 standard deviations from the mean. Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 13 / 17 68-95-99.7 Rule Given a normal distribution: Roughly 99.7% of the data values are within 3 standard deviations from the mean. Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 14 / 17 68-95-99.7 Rule Given a normal distribution: Roughly 50% of the data values are less than the mean. Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 15 / 17 68-95-99.7 Rule Given a normal distribution: Roughly 50% of the data values are greater than the mean. Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 16 / 17 Fin Fin. Josh Engwer (TTU) Statistics: Normal Distributions, 68-95-99.7 Rule 04 August 2015 17 / 17