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Distribution
The Normal Distribution Curve is a bell-shaped curve."
Normal Distribution
The Normal Distribution Curve is a bell-shaped curve.
Each band of the curve has a width of 1 Standard Deviation:
Each band of the curve has a width of 1 Standard deviation from the Mean Value.
Values less than 1 Standard Deviation away account for 68.27%.
Values less than 2 standard deviations away account for 95.45%.
Values less than 3 standard deviations away account for 99.73%.
What does it mean?
Most observations are within 1 standard deviation from the mean.
Almost all observations are within 2 standard deviations.
Practically all observations are within 3 standard deviations.
Normal Distribution Facts
Normal distribution is Symmetric. The peak always divides the distribution in half.
Normal distribution is a Probability distribution.
A lot of observations follow the normal distribution:
Normal distribution shows that values near the mean are more frequent than values far from the mean:
| Distance from the Mean Value | Percentage of the Population |
|---|---|
| 1 Standard deviation | 68.27% |
| 2 Standard deviations | 95.45% |
| 3 Standard deviations | 99.73% |
The 68–95–99.7 Rule (aka The Empirical Rule), is a shorthand to remember the percentage of values that lie within the different bands of a normal distribution.
Normal distribution is also known as the Gaussian Distribution and the Bell Curve.
The Margin of Error
Statisticians will always try to predict everything with 100% accuracy.
But, there will always be some uncertainty.
The Margin of Error is the number that quantifies this statistical uncertainty.
The more samples we collect, the lower the margin of error is:
How to Interpret Margin of Error
Suppose 55% of a sampled population say they plan to vote "Yes".
When projecting this to a whole population, you add/subtract the margin of error to give a range of possible results.
With a margin of error of 3%, you are confident that between 52% and 58% will vote "Yes".
With a margin of error of 10%, you are confident that between 45% and 65% will vote "Yes".
Skewness
Kurtosis
While skewness describes a unexpected values in one tail, kurtosis describes unexpected values in both tails.
Image: Negative kurtosis (lower than normal distribution).
Image: Positive kurtosis (higher than normal distribution).