1. **State the problem:** Calculate the standard deviation of the data set: 6, 22, 33, 88, 43, 50, 2, 78. 2. **Formula for standard deviation:** $$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2}$$ where $N$ is the number of data points, $x_i$ are the data points, and $\mu$ is the mean. 3. **Calculate the mean $\mu$:** $$\mu = \frac{6 + 22 + 33 + 88 + 43 + 50 + 2 + 78}{8} = \frac{322}{8} = 40.25$$ 4. **Calculate each squared deviation $(x_i - \mu)^2$:** - $(6 - 40.25)^2 = (-34.25)^2 = 1173.06$ - $(22 - 40.25)^2 = (-18.25)^2 = 333.06$ - $(33 - 40.25)^2 = (-7.25)^2 = 52.56$ - $(88 - 40.25)^2 = 47.75^2 = 2280.06$ - $(43 - 40.25)^2 = 2.75^2 = 7.56$ - $(50 - 40.25)^2 = 9.75^2 = 95.06$ - $(2 - 40.25)^2 = (-38.25)^2 = 1462.56$ - $(78 - 40.25)^2 = 37.75^2 = 1424.06$ 5. **Sum the squared deviations:** $$1173.06 + 333.06 + 52.56 + 2280.06 + 7.56 + 95.06 + 1462.56 + 1424.06 = 6827.98$$ 6. **Divide by $N=8$ to find variance:** $$\frac{6827.98}{8} = 853.50$$ 7. **Take the square root to find standard deviation:** $$\sigma = \sqrt{853.50} = 29.22$$ **Final answer:** The standard deviation of the data set is **29.22** (rounded to 2 decimal places).