 अम जीज़कोर्स को use करतें डिस्तीबुशन को standardize करने किब लिए अम की सीज़ीज़़न को जब जीज़्कोर्स में कनवरट कर लेते है, तो यो से further next step के अंग दर हम नीक स्थन्धडैश डिस्तीबॉशन में आपने देकाउगा के भैहासे psychological test कि लिए if the original distribution is negatively skewed, for example, then the z-scores distribution would also be skewed because we are converting the same raw score to a standard z-scores so the shape of your distribution will be exactly the same do the same as we have done in the previous examples if the distribution of your raw score is 70, 100 or 60 so when we convert it to z-scores distribution then our mean will always be 0 and the standard deviation will always be 1 all positive z-scores are above the mean and all negative z-scores will be below the mean as we have seen in the distribution that if there is a positive sign with z-scores then it means that it is above the mean if you convert the raw score to z-scores 1 then you immediately can have an idea that that the mean is above the mean standard deviation which means that if the middle point is 50% and the area from the mean to the one is 0.34% then almost 84% of the class is below it so if I tell you that z is minus 1 of an individual then you can immediately guess that the individual is below the mean standard deviation so its score will be pretty low standard deviation, the mean will be 0 and the standard deviation will always be 1 whenever we convert the distribution of the raw score to z-scores when any distribution with any mean or standard deviation is transformed into z-scores the resulting distribution will always have a mean of 1 and standard deviation of 0 this is the universal truth that when we convert any distribution to z-scores then the mean will always be 0 and the standard deviation will always be 1 one advantage of standardizing distribution is that it makes it possible to compare different scores which we have just talked about that when we convert to z-scores then we can directly compare different constructs different variables to the same person's performance on different tests to the point where they are providing and where their performance is and then we can do the same performance of the participant across different disciplines if my son has a grade in sports and what is his in mathematics and what is his in English language so what is in art and music I can compare one performance across no matter how different constructs are converted into z-scores we can directly compare them I have told you that how do we do standardization when we convert any raw data to z-scores then we convert it to standardized distribution why do we convert it? as you can see there are many test of intelligence there are your ways your ravens your autos and there are many different intelligence tests if you have done all the intelligence tests their mean and standard deviation are different then it will be hard for any person to make sense of any IQ when we tell our intelligence quotient first of all I tell you that I have 120 this means that universally all the IQ tests are converted to standardized distribution whose mean is 100 and standard deviation is 15 or 10 so when I will tell my IQ then immediately one can have an idea that if this is standardized distribution then it is above your mean similarly there are many personality tests we don't have one test so across different tests how we will make sense of my consciousness and my agreeableness so we convert a z-score distribution into a standardized distribution so the scores make more sense in universally the people who will understand where is the standing of any individual so to make a standardized distribution the first step is that we convert the original raw scores into z-scores whose formula you all know which is x-minus mean divided by standard deviation the second step is that z-scores are then converted into or transformed into new x-values how we plug in the new standardized mean and the new standardized distribution standard deviation so that it makes sense in this we convert z-scores into new raw scores in which x is equal to mean plus z into standard deviation I have solved an example for you that on a test you got a score of 70 with the mean of 60 and standard deviation of 10 so in the first step I will convert it into z-scores so that will be equal to x-minus mean which is 70-60 divided by standard deviation which is 10 so the z-score will be 1 now the first step I will transform this z-score in this distribution which I want 100 and its mean and standard deviation 10 so to convert it I will plug in values into this formula which I have done here to calculate the new x I will put I have put the mean of 100 your z-score is 1 and your standard deviation is 10 so I will plug in the values and I will calculate a new raw score it is a standardized distribution in your psychology psychological test we usually transform which means that it is universally understandable and people can relate and compare performances on different test can do as you have one more example that we talked of the distribution exactly this is the first step of the original raw score and on the other side I have converted it into z-score so shape will remain the same position will remain the same and every individual will be at the same place and then I have converted it into new raw scores meaning standardized distribution with the mean of 50 and standard deviation of 10 so the original distribution for example your zanup got a score of 43 and ali got a score of 71 with the mean of 57 and standard deviation 14 this is a test score on the first step I will calculate for zanup and ali so I have calculated their z and then on the second step I will convert them into new raw score with the mean of 50 and standard deviation of 10 but you see when I have converted them into z and then I have converted it so its shape and location and standing will remain exactly as it was before but the benefit of this is that if we do the rest it is an IQ test or more so intelligence test then we standardize the distribution universally we have the mean of 100 in IQ test and standard deviation 10 so what are the benefits the sample of z score will have the same shape as the original sample of the scores we have talked about the sample of the z score will have a mean of 0 definitely we have talked about it and its standard deviation will remain the same why we convert scores into a standardized distribution for example schoolastic aptitude test they are transformed into a standardized distribution with the mean of 500 because we transform it and make it comparable universally so that if you report an SAT score everybody has an idea of its mean of 500 what is your score so I can relate those scores I can see your standing in the distribution and that will be more meaningful and that will be more easy for me so this is how we convert into raw score into z and then z score into a standardized distribution