Z-Score Normalization – (Data Mining)
Z-Score helps in the normalization of data. If we normalize the data into a simpler form with the help of z score normalization, then it’s very easy to understand by our brains.
Z- Score Formula
How to calculate Z-Score of the following data?
| marks |
| 8 |
| 10 |
| 15 |
| 20 |
Mean = 13.25
Standard deviation = 4.6
| marks | marks after z-score normalization |
| 8 | -1.14 |
| 10 | -0.7 |
| 15 | 0.3 |
| 20 | 1.4 |
Download Excel File Calculations
How to calculate Z-Score of the following data?
How do you use a z score table?
1. We can find a specific area under the normal distribution curve.
2. We can find the z-score of the data value and use a Z-Score Table.
Z-Score Table is used to find the area.
A Z-Score Table shows the area percentage to the left of a given z-score on a standard normal distribution.
Advantages of the z score
The z-score is very useful when we are understanding the data. Some of the useful facts are mentioned below;
The z-score is a very useful statistic of the data due to the following facts;
It allows a data administrator to understand the probability of a score occurring within the normal distribution of the data.
The z-score enables a data administrator to compare two different scores that are from different normal distributions of the data.
Is a higher or lower Z score better?
Suppose we have data from two persons. Person A has a high Z score value and person B have low Z Score value. In this case, the higher Z-score indicates that Person A is far away from person B.
What does a negative and a positive z score mean?
A negative z-score indicates that the data point is below the mean.
A positive z-score indicates that the data point is above the mean.
Why is the mean of Z scores is 0?
The standard deviation of the z-scores is always 1 and similarly, the mean of the z-scores is always 1.
Z-scores values above the 0 represent that sample values are above the mean.
z-scores values below the 0 represent that sample values are below the mean.
In the case of squared z-scores, the sum of the squared z-scores is always equal to the number of z-score values.
What is the meaning of the high Z score and low Z score?
- Suppose we have a high z-score value then it means a very low probability of data above this z-score.
- Suppose we have a low z-score value then it means a very low probability of data below this z-score.
Download Important Files of Z Score Normalization
Video Lecture
99 confidence interval z score
Let’s see the 99 confidence interval z score, 95 confidence interval z score, and 90 confidence interval z score.
| Confidence Interval |
Z Score |
|
90% |
1.645 |
Z-Score to Percentile
Z-Score to Percentile formula: p=Pr(Z<z)
Let’s compute the percentile associated with a Z-score value 20.
Z-score =20
As a first step, we use a normality table to found that Pr(Z < 20) = 1
Then, in order to find the corresponding percentile we compute:
100 × Pr(Z < 20) = 100 × 1 = 100%
Therefore, it is concluded that the corresponding percentile associated to the given Z-score of Z = 20 is the 100-th percentile.
Let’s see the results graphically with the help of a diagram.
Z score table
Table of the standard normal distribution values z<=0.
Table of the standard normal distribution values z>=0.
Download Z score table in pdf.
FAQ
Which of the following is a fundamental difference between the t statistic and a z-score?
- In the case of t statistic, the sample mean in place of the population mean
- The t statistic uses the sample variance in place of the population variance
- If the null is true, some extreme observations of t are observed than z.
- The t statistic is helpful only for very large samples and z-score is helpful for all sample sizes
Answer: B
Is a standardized score necessarily a z-score?
Answer: a standardized score does not necessarily a z-score.
What conditions would produce a negative z-score?
A) a z score corresponding to an area located entirely on the right side of the curve.
B) a z score for a -ve area.
C) an area in the top 10% of the graph.
D) a z score corresponding to an area located entirely on the left side of the curve.
Answer: D