A company produces 8-pound bags of cat litter; as shown below,it gathered 5 samples with 6 bags in each sample for quality control purposes.The weights of each of the bags are listed below.Determine X-double bar $\bar{\bar{X}}$ .SHOW YOUR WORK.? $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $$\text { Bag Number of each sample }$
$\begin{array}{|c|cccccc|}
\hline \text { Sample } & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \
\hline \mathbf{1} & 7.98 & 8.34 & 8.02 & 7.94 & 8.44 & 7.68 \
\mathbf{2} & 8.33 & 8.22 & 8.08 & 8.51 & 8.41 & 8.28 \
\mathbf{3} & 7.89 & 7.77 & 7.91 & 8.04 & 8 & 7.89 \
\mathbf{4} & 8.24 & 8.18 & 7.83 & 8.05 & 7.9 & 8.16 \
\mathbf{5} & 7.87 & 8.13 & 7.92 & 7.99 & 8.1 & 7.81 \
\hline
\end{array}$ ?

Question

A company produces 8-pound bags of cat litter; as shown below,it gathered 5 samples with 6 bags in each sample for quality control purposes.The weights of each of the bags are listed below.Determine X-double bar $\bar{\bar{X}}$ .SHOW YOUR WORK.?  $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $$\text { Bag Number of each sample }$
$\begin{array}{|c|cccccc|}
\hline \text { Sample } & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \
\hline \mathbf{1} & 7.98 & 8.34 & 8.02 & 7.94 & 8.44 & 7.68 \
\mathbf{2} & 8.33 & 8.22 & 8.08 & 8.51 & 8.41 & 8.28 \
\mathbf{3} & 7.89 & 7.77 & 7.91 & 8.04 & 8 & 7.89 \
\mathbf{4} & 8.24 & 8.18 & 7.83 & 8.05 & 7.9 & 8.16 \
\mathbf{5} & 7.87 & 8.13 & 7.92 & 7.99 & 8.1 & 7.81 \
\hline
\end{array}$ ?

Quizplus · Accepted Answer

To find $\bar{\bar{X}}$, the average of all sample means, first calculate the mean of each sample, then average those means.Sample 1 mean: $\frac{7.98 + 8.34 + 8.02 + 7.94 + 8.44 + 7.68}{6} = 8.067$Sample 2 mean: $\frac{8.33 + 8.22 + 8.08 + 8.51 + 8.41 + 8.28}{6} = 8.305$Sample 3 mean: $\frac{7.89 + 7.77 + 7.91 + 8.04 + 8 + 7.89}{6} = 7.916$Sample 4 mean: $\frac{8.24 + 8.18 + 7.83 + 8.05 + 7.9 + 8.16}{6} = 8.06$Sample 5 mean: $\frac{7.87 + 8.13 + 7.92 + 7.99 + 8.1 + 7.81}{6} = 7.97$Average of sample means: $\frac{8.067 + 8.305 + 7.916 + 8.06 + 7.97}{5} = 8.0636$Rounded to two decimal places, $\bar{\bar{X}} = 8.06$.

A Company Produces 8-Pound Bags of Cat Litter; as Shown Xˉˉ\bar{\bar{X}}Xˉˉ

A Company Produces 8-Pound Bags of Cat Litter; as Shown $\bar{\bar{X}}$