If the mean of the data: 7, 8, 9, 7, 8, 7, , 8 is 8, then the variance of this data is

Question

If the mean of the data: 7, 8, 9, 7, 8, 7, \lambda , 8 is 8, then the variance of this data is

Accepted Answer

$$\overline x $$ = $${{7 + 8 + 9 + 7 + 8 + 7 + \lambda  + 8} \over 8}$$ = 8

$$ \Rightarrow $$ $\,\,\,$${{54 + \lambda } \over 8}$= 8$ \Rightarrow $$\lambda $= 10

Now variance =$\sigma $2

=${{{{\left( {7 - 8} \right)}^2} + {{\left( {8 - 8} \right)}^2} + {{\left( {9 - 8} \right)}^2} + {{\left( {7 - 8} \right)}^2} + {{\left( {8 - 8} \right)}^2} + {{\left( {7 - 8} \right)}^2} + {{\left( {10 - 8} \right)}^2} + {{\left( {8 - 8} \right)}^2}} \over 8}$$ \Rightarrow $$\sigma $2 =${{1 + 0 + 1 + 1 + 0 + 1 + 4 + 0} \over 8}$=${8 \over 8}$

Solutions · 1