Sum Squares Differences 0Bc9F8

1. **State the problem:** We need to calculate the sum of squares of the differences between each number and $0.15$: $$\sum (x_i - 0.15)^2$$ where $x_i$ are the numbers: $10.0, 9.0, 9.0, 6.0, 5.0, 3.0, 1.0, 65.0, 39.0, 1.0, 16.0, 14.0, 15.0, -4.0, -7.0, -15.0, -26.0, -56.0, -61.0, -51.0$. 2. **Formula used:** For each term, compute the difference $d_i = x_i - 0.15$, then square it: $d_i^2$. 3. **Calculate each difference and square:** - $(10.0 - 0.15)^2 = (9.85)^2 = 97.0225$ - $(9.0 - 0.15)^2 = (8.85)^2 = 78.3225$ - $(9.0 - 0.15)^2 = 78.3225$ - $(6.0 - 0.15)^2 = (5.85)^2 = 34.2225$ - $(5.0 - 0.15)^2 = (4.85)^2 = 23.5225$ - $(3.0 - 0.15)^2 = (2.85)^2 = 8.1225$ - $(1.0 - 0.15)^2 = (0.85)^2 = 0.7225$ - $(65.0 - 0.15)^2 = (64.85)^2 = 4206.0225$ - $(39.0 - 0.15)^2 = (38.85)^2 = 1509.9225$ - $(1.0 - 0.15)^2 = 0.7225$ - $(16.0 - 0.15)^2 = (15.85)^2 = 251.1225$ - $(14.0 - 0.15)^2 = (13.85)^2 = 191.8225$ - $(15.0 - 0.15)^2 = (14.85)^2 = 220.5225$ - $(-4.0 - 0.15)^2 = (-4.15)^2 = 17.2225$ - $(-7.0 - 0.15)^2 = (-7.15)^2 = 51.1225$ - $(-15.0 - 0.15)^2 = (-15.15)^2 = 229.5225$ - $(-26.0 - 0.15)^2 = (-26.15)^2 = 683.8225$ - $(-56.0 - 0.15)^2 = (-56.15)^2 = 3152.8225$ - $(-61.0 - 0.15)^2 = (-61.15)^2 = 3739.8225$ - $(-51.0 - 0.15)^2 = (-51.15)^2 = 2616.3225$ 4. **Sum all squared differences:** $$97.0225 + 78.3225 + 78.3225 + 34.2225 + 23.5225 + 8.1225 + 0.7225 + 4206.0225 + 1509.9225 + 0.7225 + 251.1225 + 191.8225 + 220.5225 + 17.2225 + 51.1225 + 229.5225 + 683.8225 + 3152.8225 + 3739.8225 + 2616.3225$$ 5. **Calculate the total sum:** $$= 97.0225 + 78.3225 + 78.3225 + 34.2225 + 23.5225 + 8.1225 + 0.7225 + 4206.0225 + 1509.9225 + 0.7225 + 251.1225 + 191.8225 + 220.5225 + 17.2225 + 51.1225 + 229.5225 + 683.8225 + 3152.8225 + 3739.8225 + 2616.3225$$ $$= 14700.5$$ **Final answer:** $$\boxed{14700.5}$$