Prob and Stat
6.1 and 6.2
μ - Sample Mean σ - Standard Deviation
Calculating Standard Deviation:
- 1. Work out the Mean (the simple average of the numbers)
- 2. Then for each number: subtract the Mean and square the result
- 3. Then work out the mean of those squared differences.
- 4. Take the square root of that and we are done!
What is the Empirical Rule?
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean.
The empirical rule can be broken down into three parts:
- 68% of data falls within the first standard deviation from the mean.
- 95% fall within two standard deviations.
- 99.7% fall within three standard deviations.
A z-score (aka, a standard score) indicates how many standard deviations an element is from the mean. A z-score can be calculated from the following formula. z = (X - μ) / σ where z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.