EXAMPLE 14 Calculating SST, the total sum of squares, in two ways

Calculate SST, the total sum of squares, for the memory score data in two ways:

  1. By using Table 8
  2. By using the fact that the sample variance of the score data (the -values) equals

Solution

  1. Table 8 shows the values for for the data in Table 7. Thus, .
  2. When we are given the variance of , we may calculate SST as follows:

Table 4.69: Table 8 Calculation of SST
Student Score
1 9 −6 36
2 10 −5 25
3 11 −4 16
4 12 −3 9
5 13 −2 4
6 14 −1 1
7 19 4 16
8 17 2 4
9 21 6 36
10 24 9 81

NOW YOU CAN DO

Exercises 11c–22c.