Final answer:
The StandardScaler method standardizes features in a dataset to have a mean of 0 and a standard deviation of 1, forming a standard normal distribution.
Z-scores are used for standardization, representing how many standard deviations a value is from the mean. An example given is the standardization of exam scores where the mean is 81, and the standard deviation is 15 points.
Step-by-step explanation:
To perform standardization of the ESOL dataset to a normal distribution, you would use the StandardScaler method. This method transforms each feature in your data (each column of the dataset) to have a mean of 0 and a standard deviation of 1, thus converting it into a form where it constitutes a standard normal distribution.
A z-score is calculated using the formula z = (x - μ) / σ, where x is the raw score, μ is the mean, and σ is the standard deviation. The z-score represents how many standard deviations an element is from the mean. If, for example, an exam score is significantly higher than the mean score, the z-score would be a positive value indicating how many standard deviations above the mean the score is.
Considering the distribution for the test where the mean score μ is 81 with a standard deviation σ of 15 points, to standardize this using the StandardScaler, you would subtract 81 from each test score and then divide by 15. This would place the distribution around the mean of 0 with a standard deviation of 1.
In a biology class with normal exam scores distribution, if Susan scored a 95 and the mean is 85 with a standard deviation of 5, her z-score would be calculated as (95 - 85) / 5, giving her a z-score of 2. This means her score is 2 standard deviations above the mean.