#Z score table free#

The formula for the standard error here will be. Here the x can be a raw score however if converting a sample mean into a z-score then the raw score is replaced by the sample mean and the standard deviation in the denominator is replaced by the standard error.

#Z score table free#

Standardisation of data thus helps us by creating a standard normal distribution with the mean of the distribution being 0 and standard deviation being 1 making the data unit free and this helps us if we want to compare data that are on different scales (example- comparing Income and Time spent on phone calling). Here the Standard Normal Distribution has all the properties that a normal distribution has along with the mean being 0, standard deviation being 1 and the total area under the curve being one. It allows us to calculate the probability of a score occurring within our normal distribution as well as enables us to compare two scores that are from different normal distributions. Standardisation thus is simply a process of converting raw scores in the distribution into standard deviation units or can say that it is a process of converting a raw observation into a z value. If the raw score is above the mean then the z-score will be positive and if it falls below the mean then it will be negative. how many standard deviations a score is above or below the mean. A z-score is a number that indicates how far above or below the mean a given score is in the distribution in the standard deviation units i.e.

Standardisation means using the mean and the standard deviation to generate a standard score also known as the z-score to help us understand where an individual score falls in relation to the other score in the distribution.