1. **Problem Statement:** We have yield data for four fertilizers over several years. We need to find the mean output per fertilizer and the grand mean for all fertilizers and years. 2. **Given Data:** Fertilizer I sums to 440, Fertilizer II sums to 424, Fertilizer III sums to 442, Fertilizer IV sums to 464. Number of observations per fertilizer = 8. 3. **Calculate Mean per Fertilizer:** $$\text{Mean}_i = \frac{\text{Sum}_i}{8}$$ - Fertilizer I mean: $$\frac{440}{8} = 55$$ - Fertilizer II mean: $$\frac{424}{8} = 53$$ - Fertilizer III mean: $$\frac{442}{8} = 55.25$$ - Fertilizer IV mean: $$\frac{464}{8} = 58$$ 4. **Calculate Grand Mean:** Total sum of all fertilizers: $$440 + 424 + 442 + 464 = 1770$$ Total observations: $$8 \times 4 = 32$$ $$\text{Grand Mean} = \frac{1770}{32} = 55.3125$$ **Final answers:** - Mean outputs: Fertilizer I = 55, II = 53, III = 55.25, IV = 58 - Grand mean = 55.3125