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I believe that z scores are the individual scores in the standard normal distribution. If we use the formula for Z score, then we will be able to discuss one particular score. The benefit of transforming data from these types of distributions for them to conform to the standard distribution is that it is easy to know where they are differentiated to the scores of others.

The Z scores roles are to show graphs or curves in the test scores among a whole grade or a classroom. The formula can be applied in helping what students need, and the subject of need, or even tell whether the curriculum for the grade is being understood and grasped by the students. This can help the administration or an individual teacher in formulating new strategies or creating new materials that can assist the student in understanding what is being tested and how to improve their grades.

The affiliation between Z score and percentage is that a z score can be twisted into a percentage, and it is a good tool to use regarding the numerous different aspects of data.

For me to understand well and apparently because I can learn better by comparing and doing tasks, I created an example of my test score that will help me figure out if I did well.

The mean is 40, and the Standard Distribution will be 10

X (my test score, original score) is 90

Z= (score-mean)/Standard Distribution

Z= (90-40)/10=5

When this data is illustrated in a graph, we would see that my score would be +3 standard distributions above the mean which is an illustration that I was able to do well on the test.


Based on what you have read, when do you think would be a more appropriate time to report a z-score rather than a percentage value?

Very nice work on your post! Because not all normal distributions share the same descriptive values, it can be hard for researchers to directly analyze their data. This is where the z transformation for the standard normal measurement can be especially useful. As you stated, “The benefit of transforming data from these types of distributions for them to conform to the standard distribution is that it is easy to know where they are differentiated to the scores of others.”

After learning new concepts from this discussion, I have a new appreciation for research statistics. I never knew what it meant when a research article explained the processes behind transforming raw data into other types of scores, but I can see how the z distribution can be helpful in comparing different sets of data by making them a standard metric and then turning them into percentages. I like the example at the end of your discussion, and you presented it in a way that was easy to follow and understand. In the case that the z score would have been negative, this would only happen if the original raw score was less than the mean. For example, if your mean was 95 instead of 40, your equation would have looked like this:

LaTeX: z=frac{90-95}{10}







= – 0.5

Because the z score is negative in this example, this means that your score would have been 1/2 of a standard distribution below the mean. I find it very helpful how the mean in the standard normal distribution is set at zero, as we can clearly see if scores are deviated either above or below the mean.

this is the other answr I have to provide:

Do you think that using the standard curve is more useful when analyzing statistical results?

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