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| 1. |
Find the sum of the deviations of the variate values 3,4,6,7,8,14 from the mean. |
| Answer» 3, 4, 6, 7, 8, 14Mean is given by: Mean={tex}\\frac{Sum of observations}{total number ofobservations}{/tex}{tex}Mean=\\frac{3+4+6+7+8+14}{6}=\\frac{42}{6}=7{/tex}Thus, {tex}{\\overline{x}}=7.{/tex}Now,{tex} {\\Delta}x_{1}={\\overline{x}-x_{1}}=7-3=4{/tex}{tex}|{\\Delta}x_{2}|=|{\\overline{x}-x_{2}}|=|7-4|=3{/tex}{tex}|{\\Delta}x_{3}|=|{\\overline{x}-x_{3}}|=|7-6|=1{/tex}{tex}|{\\Delta}x_{4}|=|{\\overline{x}-x_{4}}|=|7-7|=0{/tex}{tex}|{\\Delta}x_{5}|=|{\\overline{x}-x_{5}}|=|7-8|=1{/tex}{tex}{\\Delta}x_{6}|=|{\\overline{x}-x_{6}}|=|7-14|=7{/tex}Sum of deviations of the variate values={tex}|{\\Delta}x_{1}|+|{\\Delta}x_{2}|+|{\\Delta}x_{3}|+|{\\Delta}x_{4}|+|{\\Delta}x_{5}|+|{\\Delta}x_{6}|{/tex}=4+3+1+0+1+7=16Therefore, the sum of deviations of the variate values is 16.\xa0 | |