# Standard deviation derivation how to remove outliers

## Standard deviation derivation how to remove outliers

Standard deviation is a statistical measure that represents how much the data is spread out from the average or mean value. It is an important tool for data analysis in various fields, including finance, science, and engineering. However, outliers in the data can have a significant impact on the standard deviation calculation. In this article, we will discuss how to derive standard deviation and how to remove outliers from the data.

Deriving Standard Deviation:

To calculate standard deviation, follow these steps:

1. Calculate the mean of the data set by adding up all the values and dividing by the number of values.
2. Subtract the mean from each data point, and then square the result.
3. Calculate the sum of the squared differences.
4. Divide the sum by the number of data points minus one.
5. Take the square root of the result.

The final answer represents the standard deviation of the data set.

Removing Outliers:

Outliers are data points that are significantly different from the rest of the data set. Outliers can be caused by errors in measurement or a genuine difference in the data. Outliers can significantly impact the standard deviation, leading to inaccurate results. To remove outliers, follow these steps:

1. Determine the range of acceptable data. For example, if the data represents the weight of a person, a reasonable range would be between 90 and 200 pounds.
2. Identify any data points outside of the acceptable range.
3. Remove the outliers from the data set.
4. Recalculate the mean and standard deviation using the remaining data points.

Removing outliers can improve the accuracy of standard deviation calculation. However, it is essential to carefully consider whether an outlier is genuine data or an error in measurement. Removing genuine data can lead to inaccurate conclusions and flawed analysis.

In conclusion, standard deviation is a valuable tool for data analysis, but outliers can significantly impact the results. By carefully removing outliers, you can obtain more accurate standard deviation measurements and make more informed decisions based on the data. 