To transform the set of raw scores into a set of z-scores in order, you will need to convert them into a standard normal distribution with a mean of 0 and a standard deviation of 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 to the Postgraduate program, students need to appear in the entrance exam which is held in two batches. John appeared in both 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
John Score is given below.
| Paper | Score Obtained | Average Score | Standard deviation |
|---|---|---|---|
| Paper A | 160 | 155 | 10 |
| Paper B | 145 | 135 | 8 |
- 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 the 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’s z score in Paper A is 0.5 standard deviation above the mean of 155 marks.
John’s z score in Paper B is 1.25 standard deviation above the mean of 135 marks.
- Step 5: Conclusion
While evaluating based on the z score, we can say that John performed relatively better in Paper B as compared to Paper A.
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.
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.
