Sample Variance Population Variance So Sxx 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 10 15 17 20 xi-x -5.5 -0.5 +1.5 +4.5 (xi-x)2 30.25 0.25 2.25 20.25 53.00 Lets try now the computer friendly way xi 10 15 17 20 xi2 100 225 289 400 1014

Sample variance Population variance Sample Std Deviation 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

SUMMARY RAW DATA Sample Variance 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 10 15 17 20 f 1 3 2 xi-x -5.5714 -0.5714 +1.4285 +4.4286 (xi-x)2 31.040 0.3265 2.0406 19.6125 f.(xi-x)2 31.040 0.9795 4.0812 19.6125 55.7132 Lets try now the alternative form xi 10 15 17 20 xi2 100 225 289 400 Xi2.f 100 675 578 400 1753 With grouped classes we use the CLASS MIDPOINT

Sample variance Population variance Sample Std Deviation Population Std Deviation