where is the total frequency (the total number of data points). The term Σf·x² means you square each distinct x value, multiply by its frequency, and sum those products. Similarly, Σf·x is the sum of each distinct x multiplied by its frequency.
s2=Sxxn−1=405−1=404=10s squared equals the fraction with numerator cap S sub x x end-sub and denominator n minus 1 end-fraction equals the fraction with numerator 40 and denominator 5 minus 1 end-fraction equals 40 over 4 end-fraction equals 10 Method 2: Using the Computational Formula
While the formula above is intuitive, calculating the mean ( Sxx Variance Formula
acts as part of the denominator to normalize the covariance:
"My data," she whispered, the realization hitting her cold. "The variance of my predictor variable is too low. I'm trying to predict Y using an X that barely changes." where is the total frequency (the total number
Sxx=9+1+1+4+9=24cap S sub x x end-sub equals 9 plus 1 plus 1 plus 4 plus 9 equals 24 Method 2: Using the Computational Formula
He grabbed a dry-erase marker and marched to the whiteboard. With a squeak, he wrote out the Greek letters that had haunted Elara’s nightmares for three months: With a squeak, he wrote out the Greek
All three yield the same result. The computational form (Formula 2) is preferred when using a calculator or spreadsheet because it avoids computing each deviation separately.
: ( s_x^2 = 40 / (5-1) = 10 ). So the variance of hours studied is 10.
[ S_xx = 445 - 405 = 40 ]