Chapter 13: Q.28 (page 765)

What are the Sum of Squares and Mean Squares Factors?

Short Answer

Expert verified

The value of $S S_{Factors} = 195.6$ and $M S_{Factors} = 48.9$ .

Step by step solution

Given Information

Team 1	Team 2	Team 3	Team 4	Team 5
36	32	48	38	41
42	35	50	44	39
51	38	39	46	40

Calculate the sum of square

To find the Sum of Squares and Mean Squares Factors:

From our Table, we can calculate

$s_{1} = 129, s_{2} = 105, s_{3} = 137, s_{4} = 128, s_{5} = 120$

We now can calculate:

${SS}_{Factors} = \sum [\frac{{(s_{j})}^{2}}{n_{j}}] - \frac{{(\sum s_{j})}^{2}}{n}$

$S S_{Factors} = \frac{s_{1}^{2}}{3} + \frac{s_{2}^{2}}{3} + \frac{s_{3}^{2}}{3} + \frac{s_{4}^{2}}{3} + \frac{s_{5}^{2}}{3} - \frac{{(s_{1} + s_{2} + s_{3} + s_{4} + s_{5})}^{2}}{15}$

$where n_{1} = n_{2} = n_{3} = n_{4} = n_{5} = 3 and n = n_{1} + n_{2} + n_{3} + n_{4} + n_{5} = 15$

So, we calculate

\frac{(129)^{2}}{3} + \frac{(105)^{2}}{3} + \frac{(137)^{2}}{3} + \frac{(128)^{2}}{3} + \frac{(120)^{2}}{3} - \frac{(129 + 105 + 137 + 128 + 120)^{2}}{15}

${SS}_{Factors} = 25739.6667 - 25544.0667 = 195.6$

Calculate the mean square factors

We calculate $M S_{Factors}$ like:

$M S_{Factors} = \frac{S S_{Factors}}{k - 1}, where k = 5$

${MS}_{Factors} = \frac{195.6}{4} = 48.9$

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What are the Sum of Squares and Mean Squares Factors?

Short Answer

Step by step solution

Given Information

Calculate the sum of square

Calculate the mean square factors

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