分布
- 正規分布とは何ですか？
- 許容誤差とは何ですか？
正規分布
正規分布曲線はベル型の曲線です。
曲線の各バンドの幅は1標準偏差です。
曲線の各バンドの幅は、平均値から1標準偏差です。
1標準偏差未満の値 は68.27％を占めます。
2標準偏差未満の値は95.45％を占めます。
3標準偏差未満の値は99.73％を占めます。
どういう意味ですか？
ほとんどの観測値は、平均から1標準偏差以内です。
ほとんどすべての観測値は2標準偏差以内です。
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:
- Your IQ
- Your Weight
- Your Height
- Your Salary
- Your Blood Pressure
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.
Different margins define different ranges for where we believe the correct answers can be found.
The acceptable margin is a matter of judgment, and relative to how important the answer is.
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 68% will vote "Yes".
With a margin of error of 10%, you are confident that between 45% and 65% will vote "Yes".