sondenso wrote:
If More detail is better!
thanks!
Thanks you, you force me to think more carefully
fast (guessing) way: the more is difference between values, the more SD. In other words SD corresponds to dispersion of data. Taking both condition, we can see that dispersion of students of A class is obviously less than that of B class. So, C
usual way:
\(SD=\sqrt{\frac{\sum{(x-x_{av})^2}}{n}}\)
1) first condition says that for class A \(|x_j-x_i|>12\)
Additionally, we can states that minimum SD is (when \(x_{av}\) is evenly between \(x_i\) and \(x_j\))
\(SD_{Amin}>\sqrt{\frac{({x_j}-x_{av})^2+({x_i}-x_{av})^2}{2}}=\sqrt{\frac{6^2+6^2}{2}}=6\)
\(SD_{Amin}>6\)
2) second condition says that for class B \(|x_j-x_i|<=6\)
Additionally, we can states that maximum SD is (when \(x_{av}\) is close to one of \(x_i\) or \(x_j\))
\(SD_{Bmax}<\sqrt{\frac{({x_j}-x_{av})^2+({x_i}-x_{av})^2}{2}}=\sqrt{\frac{6^2+0^2}{2}}=\frac{6}{\sqrt{2}}\)
\(SD_{Bmin}<\frac{6}{\sqrt{2}}\)
1)&2) Combine two conditions:
\(SD_{A}=>SD_{Amin}>6>\frac{6}{\sqrt{2}}>SD_{Bmin}>=SD_{B}\)
\(SD_{A}>SD_{B}\)
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