Math Problem Solver

\[\frac{{\left( 16.39 - 10.19 \right)}^{2} + {\left( 5.15 - 10.19 \right)}^{2} + {\left( 5.22 - 10.19 \right)}^{2} + {\left( 14.0 - 10.19 \right)}^{2}}{4 - 1} = \frac{515293}{15000} = 34.3528\overline{6}\]

\[\begin{aligned}\frac{{\left( 16.39 - 10.19 \right)}^{2} + {\left( 5.15 - 10.19 \right)}^{2} + {\left( 5.22 - 10.19 \right)}^{2} + {\left( 14.0 - 10.19 \right)}^{2}}{4 - 1}& = \left(\left(16 + \frac{39}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{15}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\left(16 + \frac{39}{100} - \frac{1019}{100}\right)^{2} + \left(5 + \frac{15}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\left(\frac{1639}{100} - \frac{1019}{100}\right)^{2} + \left(5 + \frac{15}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\left(\frac{31}{5}\right)^{2} + \left(5 + \frac{15}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \left(5 + \frac{15}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \left(5 + \frac{3}{20} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \left(5 + \frac{3}{20} - \frac{1019}{100}\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \left(\frac{103}{20} - \frac{1019}{100}\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \left(- \frac{126}{25}\right)^{2} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \left(5 + \frac{22}{100} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \left(5 + \frac{11}{50} - \left(10 + \frac{19}{100}\right)\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \left(5 + \frac{11}{50} - \frac{1019}{100}\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \left(\frac{261}{50} - \frac{1019}{100}\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \left(- \frac{497}{100}\right)^{2} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \frac{247009}{10000} + \left(14 - \left(10 + \frac{19}{100}\right)\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \frac{247009}{10000} + \left(14 - \frac{1019}{100}\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \frac{247009}{10000} + \left(\frac{381}{100}\right)^{2}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{961}{25} + \frac{15876}{625} + \frac{247009}{10000} + \frac{145161}{10000}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{39901}{625} + \frac{247009}{10000} + \frac{145161}{10000}\right) \cdot \frac{1}{4 - 1}\\& = \left(\frac{35417}{400} + \frac{145161}{10000}\right) \cdot \frac{1}{4 - 1}\\& = \frac{515293}{5000} \cdot \frac{1}{4 - 1}\\& = \frac{515293}{5000} \cdot \frac{1}{3}\\& = \frac{515293}{15000}\end{aligned}\]