Variabilita 2

Za mesiac september vymeškali študenti nasledujúce počty vyučovacích hodín:
Dievčatá: 2;0;7;8;2;2;4;
Chlapci: 4;4;0;3;10;3;8;
Porovnajte variabilitu obidvoch štatistických súborov.

Správna odpoveď:

r₁ =  7,3878
r₂ =  9,6735

Postup správneho riešenia:

$$\begin{gathered} {\mu }_1=\frac{2+0+7+8+2+2+4}{7}=\frac{25}{7}=3\frac{4}{7}\doteq 3,5714 \\ {\mu }_2=\frac{4+4+0+3+10+3+8}{7}=\frac{32}{7}=4\frac{4}{7}\doteq 4,5714 \\ {e}_1=(2-{\mu }_1{)}^2+(0-{\mu }_1{)}^2+(7-{\mu }_1{)}^2+(8-{\mu }_1{)}^2+(2-{\mu }_1{)}^2+(2-{\mu }_1{)}^2+(4-{\mu }_1{)}^2=(2-\frac{25}{7}{)}^2+(0-\frac{25}{7}{)}^2+(7-\frac{25}{7}{)}^2+(8-\frac{25}{7}{)}^2+(2-\frac{25}{7}{)}^2+(2-\frac{25}{7}{)}^2+(4-\frac{25}{7}{)}^2=\frac{362}{7}=51\frac{5}{7}\doteq 51,7143 \\ {r}_1=\frac{e_1}{7}=\frac{\frac{362}{7}}{7}=\frac{362}{49}=7\frac{19}{49}=7,3878 \end{gathered}$$

$$\begin{gathered} e_2=(4-{\mu }_2{)}^2+(4-{\mu }_2{)}^2+(0-{\mu }_2{)}^2+(3-{\mu }_2{)}^2+(10-{\mu }_2{)}^2+(3-{\mu }_2{)}^2+(8-{\mu }_2{)}^2=(4-\frac{32}{7}{)}^2+(4-\frac{32}{7}{)}^2+(0-\frac{32}{7}{)}^2+(3-\frac{32}{7}{)}^2+(10-\frac{32}{7}{)}^2+(3-\frac{32}{7}{)}^2+(8-\frac{32}{7}{)}^2=\frac{474}{7}=67\frac{5}{7}\doteq 67,7143 \\ {r}_2=\frac{e_2}{7}=\frac{\frac{474}{7}}{7}=\frac{474}{49}=9\frac{33}{49}\doteq 9,6735 \\ {r}_1<r_2 \end{gathered}$$

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