Zważono jabłka z dwóch koszyków...- Zadanie 57: Matematyka z plusem 2. Zakres podstawowy i rozszerzony

Rozwiązanie

Koszyk I

Obliczmy średnią arytmetyczną wagi jabłek:

$\overline{x_{1}} = \frac{25 + 17 + 28 + 16 + 15 + 17 + 17 + 25 + 29 + 31 + 29 + 18 + 15}{13} = \frac{282}{13}$

Obliczmy odchylenie standardowe wagi jabłek

$σ_{1} = \frac{( 25 - \frac{282}{13} ) ^{2} + ( 17 - \frac{282}{13} ) ^{2} + ( 28 - \frac{282}{13} ) ^{2} + ( 16 - \frac{282}{13} ) ^{2} + ( 15 - \frac{282}{13} ) ^{2} + ( 17 - \frac{282}{13} ) ^{2} + ( 17 - \frac{282}{13} ) ^{2} + ( 25 - \frac{282}{13} ) ^{2} + ( 29 - \frac{282}{13} ) ^{2} + ( 31 - \frac{282}{13} ) ^{2} + ( 29 - \frac{282}{13} ) ^{2} + ( 18 - \frac{282}{13} ) ^{2} + ( 15 - \frac{282}{13} ) ^{2}}{13} =$

$= \frac{( \frac{43}{13} ) ^{2} + ( - \frac{61}{13} ) ^{2} + ( \frac{82}{13} ) ^{2} + ( - \frac{74}{13} ) ^{2} + ( - \frac{87}{13} ) ^{2} + ( - \frac{61}{13} ) ^{2} + ( - \frac{61}{13} ) ^{2} + ( \frac{43}{13} ) ^{2} + ( \frac{95}{13} ) ^{2} + ( \frac{121}{13} ) ^{2} + ( \frac{95}{13} ) ^{2} + ( - \frac{48}{13} ) ^{2} + ( - \frac{87}{13} ) ^{2}}{13} =$

$= \frac{\frac{1849}{169} + \frac{3721}{169} + \frac{6724}{169} + \frac{5476}{169} + \frac{7569}{169} + \frac{3721}{169} + \frac{3721}{169} + \frac{1849}{169} + \frac{9025}{169} + \frac{14641}{169} + \frac{9025}{169} + \frac{2304}{169} + \frac{7569}{169}}{13} =$

$= \frac{\frac{77194}{169}}{13} = \frac{\frac{5938}{13}}{13} = \frac{5938}{169} = \frac{5938}{13} \approx 5, 93$

Koszyk II

Obliczmy średnią arytmetyczną wagi jabłek:

$\overline{x_{2}} = \frac{23 + 23 + 24 + 19 + 21 + 15 + 25 + 24 + 24 + 21 + 25}{11} = \frac{244}{11}$

Obliczmy odchylenie standardowe wagi jabłek

$σ_{2} = \frac{( 23 - \frac{244}{11} ) ^{2} + ( 23 - \frac{244}{11} ) ^{2} + ( 24 - \frac{244}{11} ) ^{2} + ( 19 - \frac{244}{11} ) ^{2} + ( 21 - \frac{244}{11} ) ^{2} + ( 15 - \frac{244}{11} ) ^{2} + ( 25 - \frac{244}{11} ) ^{2} + ( 24 - \frac{244}{11} ) ^{2} + ( 24 - \frac{244}{11} ) ^{2} + ( 21 - \frac{244}{11} ) ^{2} + ( 25 - \frac{244}{11} ) ^{2}}{11} =$

$= \frac{( \frac{9}{11} ) ^{2} + ( \frac{9}{11} ) ^{2} + ( \frac{20}{11} ) ^{2} + ( - \frac{35}{11} ) ^{2} + ( - \frac{13}{11} ) ^{2} + ( - \frac{79}{11} ) ^{2} + ( \frac{31}{11} ) ^{2} + ( \frac{20}{11} ) ^{2} + ( \frac{20}{11} ) ^{2} + ( - \frac{13}{11} ) ^{2} + ( \frac{31}{13} ) ^{2}}{11} =$

$= \frac{\frac{81}{121} + \frac{81}{121} + \frac{400}{121} + \frac{1225}{121} + \frac{169}{121} + \frac{6241}{121} + \frac{961}{121} + \frac{400}{121} + \frac{400}{121} + \frac{169}{121} + \frac{961}{121}}{11} =$