1. **State the problem:** Calculate the mean deviation about the median for two series A and B, then compare their variability. 2. **Recall the formula for mean deviation about the median:** $$\text{Mean Deviation} = \frac{1}{n} \sum_{i=1}^n |x_i - \text{Median}|$$ where $n$ is the number of data points. 3. **Find the median of each series:** - Series A: Sort the data: 3484, 3680, 3682, 4124, 4308, 4388, 4572, 5624 Since $n=8$ (even), median is average of 4th and 5th values: $$\text{Median}_A = \frac{4124 + 4308}{2} = \frac{8432}{2} = 4216$$ - Series B: Sort the data: 186, 218, 266, 382, 408, 487, 508, 620 Median is average of 4th and 5th values: $$\text{Median}_B = \frac{382 + 408}{2} = \frac{790}{2} = 395$$ 4. **Calculate mean deviation for Series A:** Calculate absolute deviations from median 4216: $$|3484 - 4216| = 732$$ $$|3680 - 4216| = 536$$ $$|3682 - 4216| = 534$$ $$|4124 - 4216| = 92$$ $$|4308 - 4216| = 92$$ $$|4388 - 4216| = 172$$ $$|4572 - 4216| = 356$$ $$|5624 - 4216| = 1408$$ Sum of deviations: $$732 + 536 + 534 + 92 + 92 + 172 + 356 + 1408 = 3922$$ Mean deviation: $$\frac{3922}{8} = 490.25$$ 5. **Calculate mean deviation for Series B:** Absolute deviations from median 395: $$|487 - 395| = 92$$ $$|508 - 395| = 113$$ $$|620 - 395| = 225$$ $$|382 - 395| = 13$$ $$|408 - 395| = 13$$ $$|266 - 395| = 129$$ $$|186 - 395| = 209$$ $$|218 - 395| = 177$$ Sum of deviations: $$92 + 113 + 225 + 13 + 13 + 129 + 209 + 177 = 971$$ Mean deviation: $$\frac{971}{8} = 121.375$$ 6. **Compare variability:** Series A has a mean deviation of 490.25, Series B has 121.375. This means Series A is more variable around its median than Series B. **Final answer:** Mean deviation about median for Series A is $490.25$. Mean deviation about median for Series B is $121.375$. Series A shows greater variability than Series B.