1. **Problem Statement:** We are given a list of values and need to square each value and then sum all the squared values. 2. **Formula:** To square a number $x$, we calculate $x^2$. To find the sum of squares for values $x_1, x_2, \ldots, x_n$, we compute $$\sum_{i=1}^n x_i^2$$ 3. **Step-by-step Calculation:** - Square each value: $21.8^2 = 475.24$ $20.8^2 = 432.64$ $22.5^2 = 506.25$ $19.7^2 = 388.09$ $19.8^2 = 392.04$ $23.7^2 = 561.69$ $24^2 = 576$ $20.5^2 = 420.25$ $20^2 = 400$ $23.5^2 = 552.25$ $21.6^2 = 466.56$ $20.5^2 = 420.25$ $20.9^2 = 436.81$ $19.9^2 = 396.01$ $16.1^2 = 259.21$ $18.5^2 = 342.25$ $17.8^2 = 316.84$ $20.6^2 = 424.36$ $23.4^2 = 547.56$ $17.6^2 = 309.76$ $21.9^2 = 479.61$ $20.6^2 = 424.36$ $24.1^2 = 580.81$ $18.7^2 = 349.69$ $23.2^2 = 538.24$ $21.1^2 = 445.21$ $18.4^2 = 338.56$ $20.1^2 = 404.01$ $18.6^2 = 345.96$ $18.3^2 = 334.89$ $19.3^2 = 372.49$ $20.8^2 = 432.64$ $18.1^2 = 327.61$ $15.4^2 = 237.16$ $21.6^2 = 466.56$ $20.2^2 = 408.04$ $17.8^2 = 316.84$ $16.8^2 = 282.24$ $20.3^2 = 412.09$ $16.6^2 = 275.56$ 4. **Sum all squared values:** $$475.24 + 432.64 + 506.25 + 388.09 + 392.04 + 561.69 + 576 + 420.25 + 400 + 552.25 + 466.56 + 420.25 + 436.81 + 396.01 + 259.21 + 342.25 + 316.84 + 424.36 + 547.56 + 309.76 + 479.61 + 424.36 + 580.81 + 349.69 + 538.24 + 445.21 + 338.56 + 404.01 + 345.96 + 334.89 + 372.49 + 432.64 + 327.61 + 237.16 + 466.56 + 408.04 + 316.84 + 282.24 + 412.09 + 275.56 = 15394.91$$ 5. **Answer:** The sum of the squares of the given values is **15394.91**. This process helps us understand how to square numbers and sum them, which is useful in statistics and data analysis for calculating variance and other measures.