# How do you interpret z-scores?

## How do you interpret z-scores?

If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean. A negative z-score reveals the raw score is below the mean average.

What is the z-score rule?

The z-score tells us how many standard deviations x is from the mean. In fact, the “empirical rule” states that for roughly bell-shaped distributions: about 68% of the data values will have z-scores between ±1, about 95% between ±2, and about 99.7% (i.e., almost all) between ±3.

### What are the characteristics of the Z-score?

1.6. 3 General Z-Score Properties

• The mean of the z-scores is always 0.
• The standard deviation of the z-scores is always 1.
• The graph of the z-score distribution always has the same shape as the original distribution of sample values.
• The sum of the squared z-scores is always equal to the number of z-score values.

Are higher z scores better?

A Z-score can reveal to a trader if a value is typical for a specified data set or if it is atypical. In general, a Z-score below 1.8 suggests a company might be headed for bankruptcy, while a score closer to 3 suggests a company is in solid financial positioning.

## What is considered a high z-score?

A high z -score means a very low probability of data above this z -score. For example, the figure below shows the probability of z -score above 2.6 . Probability for this is 0.47% , which is less than half-percent. A low z -score means a very low probability of data below this z -score.

What happens when Z-score is too high?

So, a high z-score means the data point is many standard deviations away from the mean. This could happen as a matter of course with heavy/long tailed distributions, or could signify outliers. A good first step would be good to plot a histogram or other density estimator and take a look at the distribution.

### How do you interpret a normal distribution curve?

The area under the normal distribution curve represents probability and the total area under the curve sums to one. Most of the continuous data values in a normal distribution tend to cluster around the mean, and the further a value is from the mean, the less likely it is to occur.

Is 2 A high z-score?

Data that is two standard deviations below the mean will have a z-score of -2, data that is two standard deviations above the mean will have a z-score of +2. Data beyond two standard deviations away from the mean will have z-scores beyond -2 or 2.

## How do you know if a z-score is unusual?

As a general rule, z-scores lower than -1.96 or higher than 1.96 are considered unusual and interesting. That is, they are statistically significant outliers.

Are higher z-scores better?

A score of 1 indicates that the data are one standard deviation from the mean, while a Z-score of -1 places the data one standard deviation below the mean. The higher the Z-score, the further from the norm the data can be considered to be.