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Transform a set of raw scores into a set of z-scores

You need to transform the set of raw scores into a set of z-scores in order to convert them into a standard normal distribution with mean 0 and standard deviation 1. Transforming raw scores into standard distribution helps us to compare the two raw scores from two different distributions.

In this blog post, we will discuss, why would you want to transform a set of raw scores into a set of z-scores with examples as given below

Transform a set of raw scores into a set of z-scores

Let’s understand the importance of transforming raw scores into a set of z-score with the help of examples.

For admission in the Postgraduate program, students need to appear in the entrance exam which is held in two batches. John appeared in both the exams and he scored 160 out of 200 on paper A and 145 out of 180 on paper B.

John wants to know in which exam he performed better as compared to others?

Solution

We need to find the z-score corresponding to each paper in order to compare them.

Step 1: Collect the input parameters

PaperScore ObtainedAverage Score Standard deviation
Paper A16015510
Paper B1451358
John Score

Step 2: Using the Z-score formula

The z-score formula is

z = (x – μ )/σ

Step 3: Calculate the z-score for the given raw scores

Using the above z score formula to calculate z score for given raw score values as given below

Z-score for Paper A = (160-155)/10 = 0.5

Z-score for Paper B = (145-135)/8 = 1.25

Step 4: Interpret Z Score result

John z score in Paper A is 0.5 standard deviation above the mean.

John z score in Paper B is 1.25 standard deviation above the mean.

Step 5: Conclusion

While evaluating based on z score, we can say that John performed relatively better in Paper B as compare to Paper A.

Cool Tip: Read more on how to Calculate Z Score in Excel!

Conclusion

I hope the above article is helpful to you to understand why would you want to transform a set of raw scores into standard distributions. It will help to compare the two scores from different distributions.

Read more on how to find a z-score using TI-NSpire!

A common reason for transforming data is that data may have one or more outliers.

These are individual points in the distribution which do not fit with the rest of the data and can skew results substantially if they’re included as part of those results. Transforming data into z scores can help to remove these outliers.

Cool Tip: Read more on how to use the z table and chart!

You can find more topics about Z-Score and how to calculate z score given the area on the ZScoreGeek home page.

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