Estadística Ejemplos

3

$3$ ,

5

$5$ ,

12

$12$ ,

14

$14$ ,

18

$18$

Paso 1

La media de un conjunto de números es la suma dividida por la cantidad de términos.

\overline{x} = \frac{3 + 5 + 12 + 14 + 18}{5}

$\overline{x} = \frac{3 + 5 + 12 + 14 + 18}{5}$

Paso 2

Simplifica el numerador.

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Paso 2.1

Suma

3

$3$ y

5

$5$ .

\overline{x} = \frac{8 + 12 + 14 + 18}{5}

$\overline{x} = \frac{8 + 12 + 14 + 18}{5}$

Paso 2.2

Suma

8

$8$ y

12

$12$ .

\overline{x} = \frac{20 + 14 + 18}{5}

$\overline{x} = \frac{20 + 14 + 18}{5}$

Paso 2.3

Suma

20

$20$ y

14

$14$ .

\overline{x} = \frac{34 + 18}{5}

$\overline{x} = \frac{34 + 18}{5}$

Paso 2.4

Suma

34

$34$ y

18

$18$ .

\overline{x} = \frac{52}{5}

$\overline{x} = \frac{52}{5}$

\overline{x} = \frac{52}{5}

$\overline{x} = \frac{52}{5}$

Paso 3

Divide.

\overline{x} = 10.4

$\overline{x} = 10.4$

Paso 4

Establece la fórmula para la varianza. La varianza de un conjunto de valores es una medida de la propagación de sus valores.

s^{2} = \sum_{i = 1}^{n} \frac{{(x_{i} - x_{a v g})}^{2}}{n - 1}

$s^{2} = \sum_{i = 1}^{n} \frac{{(x_{i} - x_{a v g})}^{2}}{n - 1}$

Paso 5

Establece la fórmula para la varianza de este conjunto de números.

s = \frac{{(3 - 10.4)}^{2} + {(5 - 10.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{{(3 - 10.4)}^{2} + {(5 - 10.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6

Simplifica el resultado.

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Paso 6.1

Simplifica el numerador.

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Paso 6.1.1

Resta

10.4

$10.4$ de

3

$3$ .

s = \frac{{(- 7.4)}^{2} + {(5 - 10.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{{(- 7.4)}^{2} + {(5 - 10.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.2

Eleva

- 7.4

$- 7.4$ a la potencia de

2

$2$ .

s = \frac{54.76 + {(5 - 10.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + {(5 - 10.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.3

Resta

10.4

$10.4$ de

5

$5$ .

s = \frac{54.76 + {(- 5.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + {(- 5.4)}^{2} + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.4

Eleva

- 5.4

$- 5.4$ a la potencia de

2

$2$ .

s = \frac{54.76 + 29.16 + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + 29.16 + {(12 - 10.4)}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.5

Resta

10.4

$10.4$ de

12

$12$ .

s = \frac{54.76 + 29.16 + {1.6}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + 29.16 + {1.6}^{2} + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.6

Eleva

1.6

$1.6$ a la potencia de

2

$2$ .

s = \frac{54.76 + 29.16 + 2.56 + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + 29.16 + 2.56 + {(14 - 10.4)}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.7

Resta

10.4

$10.4$ de

14

$14$ .

s = \frac{54.76 + 29.16 + 2.56 + {3.6}^{2} + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + 29.16 + 2.56 + {3.6}^{2} + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.8

Eleva

3.6

$3.6$ a la potencia de

2

$2$ .

s = \frac{54.76 + 29.16 + 2.56 + 12.96 + {(18 - 10.4)}^{2}}{5 - 1}

$s = \frac{54.76 + 29.16 + 2.56 + 12.96 + {(18 - 10.4)}^{2}}{5 - 1}$

Paso 6.1.9

Resta

10.4

$10.4$ de

18

$18$ .

s = \frac{54.76 + 29.16 + 2.56 + 12.96 + {7.6}^{2}}{5 - 1}

$s = \frac{54.76 + 29.16 + 2.56 + 12.96 + {7.6}^{2}}{5 - 1}$

Paso 6.1.10

Eleva

7.6

$7.6$ a la potencia de

2

$2$ .

s = \frac{54.76 + 29.16 + 2.56 + 12.96 + 57.76}{5 - 1}

$s = \frac{54.76 + 29.16 + 2.56 + 12.96 + 57.76}{5 - 1}$

Paso 6.1.11

Suma

54.76

$54.76$ y

29.16

$29.16$ .

s = \frac{83.92 + 2.56 + 12.96 + 57.76}{5 - 1}

$s = \frac{83.92 + 2.56 + 12.96 + 57.76}{5 - 1}$

Paso 6.1.12

Suma

83.92

$83.92$ y

2.56

$2.56$ .

s = \frac{86.48 + 12.96 + 57.76}{5 - 1}

$s = \frac{86.48 + 12.96 + 57.76}{5 - 1}$

Paso 6.1.13

Suma

86.48

$86.48$ y

12.96

$12.96$ .

s = \frac{99.44 + 57.76}{5 - 1}

$s = \frac{99.44 + 57.76}{5 - 1}$

Paso 6.1.14

Suma

99.44

$99.44$ y

57.76

$57.76$ .

s = \frac{157.2}{5 - 1}

$s = \frac{157.2}{5 - 1}$

s = \frac{157.2}{5 - 1}

$s = \frac{157.2}{5 - 1}$

Paso 6.2

Simplifica la expresión.

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Paso 6.2.1

Resta

1

$1$ de

5

$5$ .

s = \frac{157.2}{4}

$s = \frac{157.2}{4}$

Paso 6.2.2

Divide

157.2

$157.2$ por

4

$4$ .

s = 39.3

$s = 39.3$

s = 39.3

$s = 39.3$

s = 39.3

$s = 39.3$

Paso 7

Aproxima el resultado.

s^{2} \approx 39.3

$s^{2} \approx 39.3$

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