How is a sample value standardized?
Do you do so by using the z-score formula, which is the value subtracted by the mean of all the data values divided by the std deviation of the sample?
Yes, you are correct. To standardize a sample value, you can use the z-score formula. The z-score is calculated by subtracting the mean of all the data values from the value you want to standardize, and then dividing that difference by the standard deviation of the sample.
Here is the z-score formula:
z = (x - μ) / σ
Where:
z = standardized value (z-score)
x = value to be standardized
μ = mean of all the data values
σ = standard deviation of the sample
To standardize a sample value using the z-score formula, follow these steps:
1. Calculate the mean (μ) of all the data values in the sample.
2. Calculate the standard deviation (σ) of the sample.
3. Subtract the mean (μ) from the value you want to standardize (x).
4. Divide the difference by the standard deviation (σ).
5. The result will be the standardized value (z-score).
By standardizing the data using the z-score formula, you transform the variable into a standard normal distribution with a mean of 0 and a standard deviation of 1. This is helpful for comparing different values within the sample or across different samples.