Sxx Calculator

Sxx Calculator

Sxx Calculator

Enter a list of x-values to calculate \( S_{xx} \), which is the sum of the squared differences of each x-value from the mean.

Sxx: 0

What is \( S_{xx} \)?

In statistics, \( S_{xx} \) represents the sum of the squared deviations of each x-value from the mean of x-values. It is used to measure the spread or variability of data in a dataset. Mathematically, \( S_{xx} \) is calculated as:

\[ S_{xx} = \sum (x_i - \bar{x})^2 \]

where:

  • \( x_i \) represents each individual x-value,
  • \( \bar{x} \) is the mean of the x-values,
  • \( \sum \) represents the summation across all x-values.

Real-Life Example

Suppose we want to analyze the number of hours a group of students spends studying for exams. We record their study hours: 4, 7, 5, 8, 12, 13, 14, 12, 16, and 19 hours. We can calculate \( S_{xx} \) for this data to understand how varied their study hours are from the average study time.

A larger \( S_{xx} \) value would indicate a high variability in study hours, meaning students spend very different amounts of time studying, while a smaller \( S_{xx} \) suggests that students' study times are close to the average.

Further Reading