1. 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

2. 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

3. Sample variance
Population variance
Sample Std Deviation
Population Std Deviation

4. 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

5. SUMMARY RAW DATA Sample Variance RAW DATA Population Variance
GROUPED DATA
Sample Variance
GROUPED DATA
Population Variance

6. 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
(xi-x)2
31.040
0.3265
2.0406
f.(xi-x)2
31.040
0.9795
4.0812
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

7. Sample variance
Population variance
Sample Std Deviation
Population Std Deviation