Math Problem Solver

\[\frac{{\left( 2.76 - 4.11 \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1} = \frac{89387}{12500} = 7.15096\]

\[\begin{aligned}\frac{{\left( 2.76 - 4.11 \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}& = \left(\left(2 + \frac{76}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{72}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\left(2 + \frac{19}{25} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{72}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\left(2 + \frac{19}{25} - \frac{411}{100}\right)^{2} + \left(3 + \frac{72}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\left(\frac{69}{25} - \frac{411}{100}\right)^{2} + \left(3 + \frac{72}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\left(- \frac{27}{20}\right)^{2} + \left(3 + \frac{72}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \left(3 + \frac{72}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \left(3 + \frac{18}{25} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \left(3 + \frac{18}{25} - \frac{411}{100}\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \left(\frac{93}{25} - \frac{411}{100}\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \left(- \frac{39}{100}\right)^{2} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \left(1 + \frac{5}{10} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \left(1 + \frac{1}{2} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \left(1 + \frac{1}{2} - \frac{411}{100}\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \left(\frac{3}{2} - \frac{411}{100}\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \left(- \frac{261}{100}\right)^{2} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \left(3 + \frac{37}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \left(3 + \frac{37}{100} - \frac{411}{100}\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \left(\frac{337}{100} - \frac{411}{100}\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \left(- \frac{37}{50}\right)^{2} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \left(9 + \frac{25}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \left(9 + \frac{1}{4} - \left(4 + \frac{11}{100}\right)\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \left(9 + \frac{1}{4} - \frac{411}{100}\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \left(\frac{37}{4} - \frac{411}{100}\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \left(\frac{257}{50}\right)^{2} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \left(4 + \frac{8}{100} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \left(4 + \frac{2}{25} - \left(4 + \frac{11}{100}\right)\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \left(4 + \frac{2}{25} - \frac{411}{100}\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \left(\frac{102}{25} - \frac{411}{100}\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \left(- \frac{3}{100}\right)^{2}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{729}{400} + \frac{1521}{10000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \frac{9}{10000}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{9873}{5000} + \frac{68121}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \frac{9}{10000}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{87867}{10000} + \frac{1369}{2500} + \frac{66049}{2500} + \frac{9}{10000}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{93343}{10000} + \frac{66049}{2500} + \frac{9}{10000}\right) \cdot \frac{1}{6 - 1}\\& = \left(\frac{357539}{10000} + \frac{9}{10000}\right) \cdot \frac{1}{6 - 1}\\& = \frac{89387}{2500} \cdot \frac{1}{6 - 1}\\& = \frac{89387}{2500} \cdot \frac{1}{5}\\& = \frac{89387}{12500}\end{aligned}\]