1. Let's restate the problem: Calculate the sample standard deviation of the data set $\{2,4,4,4,5,5,7,9\}$ using a table. 2. Recall the formula for sample standard deviation: $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $n$ is the sample size and $\bar{x}$ is the sample mean. 3. First, calculate the mean: $$\bar{x} = \frac{2+4+4+4+5+5+7+9}{8} = 5$$ 4. Now, create a table with columns: Data point $x_i$, Deviation $(x_i - \bar{x})$, Squared deviation $(x_i - \bar{x})^2$. | $x_i$ | $x_i - \bar{x}$ | $(x_i - \bar{x})^2$ | |-------|-----------------|---------------------| | 2 | 2 - 5 = -3 | $(-3)^2 = 9$ | | 4 | 4 - 5 = -1 | $(-1)^2 = 1$ | | 4 | -1 | 1 | | 4 | -1 | 1 | | 5 | 0 | 0 | | 5 | 0 | 0 | | 7 | 7 - 5 = 2 | $2^2 = 4$ | | 9 | 9 - 5 = 4 | $4^2 = 16$ | 5. Sum the squared deviations: $$9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32$$ 6. Calculate the sample variance: $$s^2 = \frac{32}{8 - 1} = \frac{32}{7} \approx 4.57$$ 7. Finally, calculate the sample standard deviation: $$s = \sqrt{4.57} \approx 2.14$$ Final answer: The sample standard deviation of the data set is approximately $2.14$.