Question 9.1: For the data in Table 9.1, find I, J1, ... , JI, N, X23, X3....

Principles of Statistics for Engineers and Scientists

For the data in Table 9.1, find I, $J_1, … , J_I, N, X_{23}, \bar{X}_3., \bar{X} ..$ ·

TABLE 9.1 Brine II hardness of welds using four different fluxes
Flux	Sample Values					Sample Mean	Sample Standard Deviation
A	250	264	256	260	239	253.8	9.7570
B	263	254	267	265	267	263.2	5.4037
C	257	279	269	273	277	271.0	8.7178
D	253	258	262	264	273	262.0	7.4498

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There are four samples, so $I = 4$ . Each sample contains five observations, so $J_1 = J_2 = J_3 = J_4 = 5$ . The total number of observations is N = 20. The quantity X $_{23}$ is the third observation in the second sample, which is 267. The quantity $\bar{X}_3$ . is the sample mean of the third sample. This value is $\bar{X}_3 = 271.0$ . Finally, we use Equation (9.3) to compute the sample grand mean $\bar{X}_{..}.$

$\bar{X}_{.,}=\frac{\sum_{i=1}^l J_i \bar{X}_i}{N}$ (9.3)

$\begin{aligned}\bar{X}_{. .}&=\frac{(5)(253.8)+(5)(263.2)+(5)(271.0)+(5)(262.0)}{20}\\&=262.5\end{aligned}$

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