Both sets of values have an average of 18 . Is Set A's standard deviation smaller, larger, or about the same as Set B's? Hint: A person can answer this question mostly by looking at the values without performing any substantial calculations. Set A: \( 1 \begin{array}{llllllllll}14 & 16 & 17 & 19 & 20 & 22 & \text { Set B: } 4 & 8 & 10 & 26 \\ 28 & 32\end{array} \)

To determine which set has a smaller standard deviation, let's analyze the spread of each set's values relative to their common mean of 18. **Set A: 14, 16, 17, 19, 20, 22** - **Differences from the mean (18):** - 14 → -4 - 16 → -2 - 17 → -1 - 19 → +1 - 20 → +2 - 22 → +4 - **Range of differences:** -4 to +4 **Set B: 4, 8, 10, 26, 28, 32** - **Differences from the mean (18):** - 4 → -14 - 8 → -10 - 10 → -8 - 26 → +8 - 28 → +10 - 32 → +14 - **Range of differences:** -14 to +14 **Analysis:** - **Set A** has values that are **closer** to the mean, with differences ranging from -4 to +4. - **Set B** has values that are **further** from the mean, with differences ranging from -14 to +14. Since standard deviation measures the average distance of each data point from the mean, a smaller spread (as seen in Set A) results in a smaller standard deviation. Conversely, a larger spread (as seen in Set B) results in a larger standard deviation. **Conclusion:** **Set A** has a smaller standard deviation compared to **Set B**. **Answer:** Set A’s values are closer to the mean, so its standard deviation is smaller than Set B’s.