miniaufgabe.js
==== 17. Februar 2020 bis 21. Februar 2020 ====
=== Montag 17. Februar 2020 ===
Berechnen Sie den Mittelwert $\mu$ und den Median $\tilde x$ für die folgenden zwei Wertereihen.
miniAufgabe("#exomeanmed","#solmeanmed",
[["a) 12, 18, 11, 11, 8 b) 5, 8, 4, 10, 8, 31 ", "a) $\\mu = 12$, $\\tilde x = 11$ b) $\\mu = 11$, $\\tilde x = 8$ "], ["a) 24, 15, 22, 26, -2 b) 10, 8, 15, 6, 12, 27 ", "a) $\\mu = 17$, $\\tilde x = 22$ b) $\\mu = 13$, $\\tilde x = 11$ "], ["a) 13, 8, 6, 5, 18 b) 15, 2, 7, 8, 10, 24 ", "a) $\\mu = 10$, $\\tilde x = 8$ b) $\\mu = 11$, $\\tilde x = 9$ "], ["a) 18, 12, 11, 18, 1 b) 20, 16, 7, 14, 14, 1 ", "a) $\\mu = 12$, $\\tilde x = 12$ b) $\\mu = 12$, $\\tilde x = 14$ "], ["a) 15, 22, 13, 19, 6 b) 16, 10, 14, 12, 19, -5 ", "a) $\\mu = 15$, $\\tilde x = 15$ b) $\\mu = 11$, $\\tilde x = 13$ "], ["a) 21, 13, 10, 8, 23 b) 11, 18, 11, 17, 17, 34 ", "a) $\\mu = 15$, $\\tilde x = 13$ b) $\\mu = 18$, $\\tilde x = 17$ "], ["a) 18, 17, 22, 23, 0 b) 10, 12, 12, 14, 6, 18 ", "a) $\\mu = 16$, $\\tilde x = 18$ b) $\\mu = 12$, $\\tilde x = 12$ "], ["a) 25, 17, 13, 16, 19 b) 16, 14, 17, 16, 23, 16 ", "a) $\\mu = 18$, $\\tilde x = 17$ b) $\\mu = 17$, $\\tilde x = 16$ "], ["a) 11, 8, 9, 10, 12 b) 19, 13, 20, 18, 17, 15 ", "a) $\\mu = 10$, $\\tilde x = 10$ b) $\\mu = 17$, $\\tilde x = \\frac{35}{2} = 17.5$ "], ["a) 14, 1, 7, 14, 14 b) 10, 13, 13, 21, 16, 17 ", "a) $\\mu = 10$, $\\tilde x = 14$ b) $\\mu = 15$, $\\tilde x = \\frac{29}{2} = 14.5$ "]],
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=== Donnerstag 20. Februar 2020 ===
Berechnen Sie Standardabweichung der folgenden Wertereihe.
miniAufgabe("#exostandardabweichung","#solstandardabweichung",
[["20, 17, 13, 21, 9", "$\\mu = 16$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(16+1+9+25+49\\right) = \\frac{1}{4}\\cdot 100 = 25$ also $\\sigma = \\sqrt{25} = 5$"], ["18, 17, 20, 18, 12", "$\\mu = 17$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+0+9+1+25\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["7, 15, 13, 13, 12", "$\\mu = 12$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(25+9+1+1+0\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["21, 21, 18, 13, 7", "$\\mu = 16$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(25+25+4+9+81\\right) = \\frac{1}{4}\\cdot 144 = 36$ also $\\sigma = \\sqrt{36} = 6$"], ["15, 17, 14, 15, 9", "$\\mu = 14$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+9+0+1+25\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["14, 20, 14, 12, 15", "$\\mu = 15$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+25+1+9+0\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["11, 6, 14, 12, 12", "$\\mu = 11$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(0+25+9+1+1\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["13, 14, 9, 7, 17", "$\\mu = 12$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+4+9+25+25\\right) = \\frac{1}{4}\\cdot 64 = 16$ also $\\sigma = \\sqrt{16} = 4$"], ["21, 15, 15, 16, 13", "$\\mu = 16$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(25+1+1+0+9\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["15, 17, 11, 13, 4", "$\\mu = 12$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(9+25+1+1+64\\right) = \\frac{1}{4}\\cdot 100 = 25$ also $\\sigma = \\sqrt{25} = 5$"]],
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