Sum of Squared Deviations Calculator

What Is the Sum of Squared Deviations?

The Sum of Squared Deviations (SSD) is a measure of data dispersion. It quantifies the variability of a dataset by summing the squared differences between each data point and the dataset's mean. The formula is: \( \text{SSD} = \sum_{i=1}^{n} (x_i - \bar{x})^2 \) Where:

• \( x_i \) represents each value in the dataset,
• \( \bar{x} \) is the mean of the dataset,
• \( n \) is the total number of data points.

How to Calculate the SSD

1. Calculate the Mean: Find the average value of the dataset (\( \bar{x} \)).
2. Compute Squared Deviations: For each data point \( x_i \), calculate the squared difference from the mean \( (x_i - \bar{x})^2 \).
3. Sum the Results: Add all the squared deviations to get the SSD.

Example: Compute the SSD of data set [4, 8, 6, 5, 3]