represents the of a single variable from its sample mean (

∑xi2=4+16+36+64+100=220sum of x sub i squared equals 4 plus 16 plus 36 plus 64 plus 100 equals 220

The Sxx variance formula, also known as the sum of squares of deviations from the mean, is a statistical formula used to calculate the variance of a dataset. Here's the text-based formula:

The sum of squared deviations from the mean is 33.5.

∑xinthe fraction with numerator sum of x sub i and denominator n end-fraction

The Sxx variance formula has numerous applications in statistics, data analysis, and engineering. Some of the key applications include:

If you are calculating this for a data set, it is often best to use the (Method B) to keep decimals to a minimum until the final step.

In regression analysis, you map the relationship between an independent variable ( ) and a dependent variable ( ). To find the slope ( ) of the best-fit line, you must use Sxxcap S sub x x end-sub alongside its counterpart, Sxycap S sub x y end-sub (the sum of products):

s squared equals the fraction with numerator cap S x x and denominator n minus 1 end-fraction A Quick Example If your data is correlation coefficient

| Term | Formula | |------|---------| | Sxx (definition) | ( \sum (x_i - \barx)^2 ) | | Sxx (computational) | ( \sum x_i^2 - \frac(\sum x_i)^2n ) | | Sample variance | ( s_x^2 = \fracS_xxn-1 ) | | Population variance (if known μ) | ( \sigma^2 = \fracS_xxn ) (but rare in practice) |

s=Sxxn−1s equals the square root of the fraction with numerator cap S sub x x end-sub and denominator n minus 1 end-fraction end-root Statistical Metric What it Measures Sxxcap S sub x x end-sub Total raw variation (Sum of Squares)

This version is the most intuitive because it shows exactly what the value represents: