 # Difference between Standard Deviation and Z-score

## Standard Deviation

Standard deviation is defined as the total amount of variability that is present within any given data set. It helps to show the total extent to which individual data points in the data set vary from the mean. A high standard deviation also means that a majority of the data points will deviate from the norm. It means that either the investment will underperform or outperform similar securities. A low standard deviation implies that most of the data points get clustered near the norm, and the returns will also be closer to the expected results.

The investors are expecting that the benchmark index fund will have a low standard deviation. However, with the growth funds, the deviation generally should be higher because the management will tend to make more aggressive moves in order to capture the returns. As with the other investments, any higher returns result in the equating of the higher investment risks. The standard deviation can also be visualised as a bell curve. A flatter and more spread-out bell curve represent a larger standard deviation and a steeper; a taller bell curve represents a smaller standard deviation. To calculate the actual standard deviation, it is important to first calculate the total difference between every data point and the mean. The differences then get squared, summed as well as averaged to help produce the variance. The standard deviation is thus the square root of variance.

## Z-Score

Z-Score (also known as the standard score) is defined as the total number of standard deviations of any given data point that lies below or above the mean. The mean is defined as the average of all the values in a group that are added together, and they then get divided by the total number of items present in the group.

To calculate the real z-score, the mean is deducted from each individual data point, and then the final result gets divided by the value of standard deviation. If the z-score is zero, it implies that the mean and the data points are equal. The main benefit of a z-score is that it helps to offer the analysts a method to make a comparison data against the norm. The financial information of any company becomes more meaningful when a stakeholder gets enough to know how to compare it with the other organisations within the industry. The z-score results of zero help to indicate the final data point that is being analysed is the exact average which is situated among the norm. A z-score of one implies that the final data is one standard deviation above the mean, while a z-score of minus one points out the fact that the data is one standard deviation below the mean. The higher the z-score, the farther the data is considered to be from the actual norm. In investing, it is important to note that when the z-score is higher, it is indicative of the fact that the expected returns will either get volatile or they are likely to be more different from expectations.

## Difference between Standard Deviation and Z-Score

Both the standard deviation and z-scores are very important for the purpose of calculations. The statisticians can understand a lot about a company by analysing these data points. However, there are some major areas of difference between standard deviation and z-score, and we should focus on them below to get a better understanding of the topic:

 Standard Deviation Z-Score Definition Standard deviation is defined as a statistical measure that helps to show how the elements are dispersed around the mean or average of a data set. Z-Score is defined as a statistical measure that helps to show how far away any value within a data set is situated from the mean. Purpose The main purpose of standard deviation is to indicate whether a particular investment will perform or not. As such, it is mostly a predictive calculation. The main purpose of a z-score is to help understand if a trader can gauge the volatility of securities in the market.

## Conclusion

There are a number of points of difference between standard deviation and z-score. But both of them have a very important role in financial transactions, and the statisticians use them for important purposes. With the advancement of technology and statistics, the role of both these measures continues to be vital for the success or failure of any business transaction.