![]() 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. 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.
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