Author
Home > Science > What is the Difference Between Standard Deviation and Mean?

Guilherme Mazui

•3 minutes to read

What is the Difference Between Standard Deviation and Mean?

🆚 Go to Comparative Table 🆚

The main difference between standard deviation and mean lies in what they represent and how they are used.

  • Standard Deviation: This is a descriptive statistic that estimates the scatter of values around the sample mean. It represents the average deviation of the individual data points from the mean. If the standard deviation is low, it indicates that the data points are close to the mean, and the data is said to be concentrated or clustered. Conversely, a high standard deviation indicates that the data points are spread out and the data is diffuse.
  • Mean: The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding all the values in the dataset and dividing the sum by the number of values. The mean is often used to provide a snapshot of the central value, and it can be affected by outliers.

In summary, the standard deviation tells us about the spread or dispersion of the data around the mean, while the mean gives us the average value of the data. Both statistics are essential for understanding the characteristics of a dataset, and they are often used together to provide a comprehensive understanding of the data.

On this page
  • What is the Difference Between Standard Deviation and Mean?
  • Comparative Table: Standard Deviation vs Mean

    • Comparative Table: Standard Deviation vs Mean

    The main difference between standard deviation and mean lies in the information they provide about a dataset. Here is a table summarizing the key differences between the two concepts:

    Feature Mean Standard Deviation
    Definition The mean is a measure of the center of a dataset, representing the average value of the data points. The standard deviation is a measure of the dispersion or spread of the data points around the mean.
    Formula To calculate the mean, add up all the values in the dataset and divide the sum by the number of values. To calculate the standard deviation, find the difference between each data point and the mean, square these differences, sum them up, and divide by the number of values minus one. Then, take the square root of the result.
    Interpretation The mean helps to understand the central tendency of a dataset, i.e., the value that a typical data point would have. The standard deviation helps to understand how much the data points deviate from the mean, or the average distance between a data point and the mean.
    Symbol Represented by $$\bar{x}$$ Represented by $$\sigma$$

    In summary, the mean provides information about the central value of a dataset, while the standard deviation provides information about how spread out the data points are around the mean. Both measures are essential for understanding and analyzing datasets, but they serve different purposes.

    Read more:

    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.