Example 14

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:

By using Table 8
By using the fact that the sample variance of the score data (the $y$ -values) equals $25 \frac{1}{3}$

Solution

Table 8 shows the values for $(y - \bar{y}) = (y - 15)$ for the data in Table 7. Thus, $SST = {\sum (y - \bar{y})}^{2} = 228$ .
When we are given the variance of $y$ , we may calculate SST as follows:

$SST = (n - 1) s^{2} = (10 - 1) (25 \frac{1}{3}) = 228$

Table 4.69: Table 8 Calculation of SST

Student	Score $(y)$	$(y - \bar{y})$	${(y - \bar{y})}^{2}$
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
		$SST = Σ {(y - \bar{y})}^{2} = 228$

NOW YOU CAN DO

Exercises 11c–22c.