Question

3 out of 5 observations of a data set are known to be 10, 10, 10. The mean and the variance of this data are both 10. Find the remaining values.

• A. 10 , 10
• B. 5, 15
• C. 2, 18
• D. 12, 8

Answer 1

The correct option is B 5, 15

$\mathrm{Let}\mathrm{the}\mathrm{other}\mathrm{two}\mathrm{values}\mathrm{be}x\mathrm{and}y.\mathrm{Mean}=\frac{\sum _{}{x}_i}{n}=\frac{10+10+10+x+y}{5}=10\Rightarrow x+y=20\mathrm{Variance}=\frac{\sum _{}{\left(x_i-\overline{x}\right)}^2}{n}=\frac{0+0+0+{\left(x-10\right)}^2+{\left(y-10\right)}^2}{5}=10\Rightarrow {\left(x-10\right)}^2+{\left(10-x\right)}^2=50{\left(x-10\right)}^2=25x=5\mathrm{or}x=15\mathrm{Therefore},y=15\mathrm{or}y=5\mathrm{So},\mathrm{the}\mathrm{remaining}\mathrm{two}\mathrm{values}\mathrm{are}5,15$