1. **Problem Statement:** We are given a list of values and need to square each value and then add all the squared values together. 2. **Formula:** For values $x_1, x_2, \ldots, x_n$, the sum of squares is given by: $$\sum_{i=1}^n x_i^2 = x_1^2 + x_2^2 + \cdots + x_n^2$$ 3. **Step-by-step calculation:** - Square each value: $22.8^2 = 519.84$ $25.8^2 = 665.64$ $23.5^2 = 552.25$ $20.7^2 = 428.49$ $20.8^2 = 432.64$ $24.7^2 = 610.09$ $27^2 = 729$ $22.5^2 = 506.25$ $21^2 = 441$ $28.5^2 = 812.25$ $22.6^2 = 510.76$ $24.5^2 = 600.25$ $20.9^2 = 436.81$ $18.9^2 = 357.21$ $16.1^2 = 259.21$ $19.5^2 = 380.25$ $17.8^2 = 316.84$ $22.6^2 = 510.76$ $24.4^2 = 595.36$ $17.6^2 = 309.76$ $21.9^2 = 479.61$ $22.6^2 = 510.76$ $25.1^2 = 630.01$ $18.7^2 = 349.69$ $24.2^2 = 585.64$ $23.1^2 = 533.61$ $18.4^2 = 338.56$ $21.1^2 = 445.21$ $18.6^2 = 345.96$ $18.3^2 = 334.89$ $19.3^2 = 372.49$ $22.8^2 = 519.84$ $18.1^2 = 327.61$ $15.4^2 = 237.16$ $23.6^2 = 556.96$ $21.2^2 = 449.44$ $17.8^2 = 316.84$ $16.8^2 = 282.24$ $20.3^2 = 412.09$ $18.6^2 = 345.96$ 4. **Add all squared values:** $$519.84 + 665.64 + 552.25 + 428.49 + 432.64 + 610.09 + 729 + 506.25 + 441 + 812.25 + 510.76 + 600.25 + 436.81 + 357.21 + 259.21 + 380.25 + 316.84 + 510.76 + 595.36 + 309.76 + 479.61 + 510.76 + 630.01 + 349.69 + 585.64 + 533.61 + 338.56 + 445.21 + 345.96 + 334.89 + 372.49 + 519.84 + 327.61 + 237.16 + 556.96 + 449.44 + 316.84 + 282.24 + 412.09 + 345.96 = 16388.92$$ 5. **Final answer:** The sum of the squares of the given values is **16388.92**. This method ensures each value is squared correctly and then summed to get the total sum of squares.