Sample Variance So Sxx Population Variance can be

Sample Variance So Sxx Population Variance can be written in different forms that are faster to calculate And for grouped data Sxx can be written as

Example Calculate Sxx for the following data and therefore the Sample and Population variance xi xi-x (xi-x)2 10 -5. 5 30. 25 15 -0. 5 0. 25 17 +1. 5 2. 25 20 +4. 5 20. 25 xi xi 2 10 100 15 225 17 289 20 400 1014 53. 00 Lets try now the computer friendly way

Sample variance Sample Std Deviation Population variance Population Std Deviation

Calculator friendly versions So Sxx can be written in different forms that are faster to calculate And for grouped data Sxx can be written as

RAW DATA Sample Variance SUMMARY RAW DATA Population Variance GROUPED DATA Sample Variance GROUPED DATA Population Variance

Example- frequency data Calculate Sxx for the following data and therefore the Sample and Population variance xi f xi-x (xi-x)2 10 1 -5. 5714 31. 040 15 3 -0. 5714 0. 3265 0. 9795 17 2 +1. 4285 2. 0406 4. 0812 20 1 +4. 4286 19. 6125 xi xi 2 Xi 2. f 10 100 15 225 675 17 289 578 20 400 1753 f. (xi-x)2 Lets try now the alternative form 55. 7132 With grouped classes we use the CLASS MIDPOINT

Sample variance Sample Std Deviation Population variance Population Std Deviation