# Z-Score Normalization

## 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.

## How to calculate Z-Score of the following data?

 marks 8 10 15 20

Mean = 13.25

4.6

 marks marks after z-score normalization 8 -1.14 10 -0.7 15 0.3 20 1.4

## 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.

PDF

Slides Presentation

Excel File Calculations

## 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% 95% 99% 1.645 1.96 2.576

## 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.

FAQ

Which of the following is a fundamental difference between the t statistic and a z-score?

1. In the case of t statistic, the sample mean in place of the population mean
2. The t statistic uses the sample variance in place of the population variance
3. If the null is true, some extreme observations of t are observed than z.
4. The t statistic is helpful only for very large samples and z-score is helpful for all sample sizes

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.