Matemática discreta Ejemplos

8

$8$ ,

47

$47$ ,

10

$10$ ,

50

$50$ ,

38

$38$ ,

23

$23$ ,

28

$28$ ,

27

$27$ ,

34

$34$ ,

28

$28$

Paso 1

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

¯ x = \frac{8 + 47 + 10 + 50 + 38 + 23 + 28 + 27 + 34 + 28}{10}

$\overline{x} = \frac{8 + 47 + 10 + 50 + 38 + 23 + 28 + 27 + 34 + 28}{10}$

Paso 2

Simplifica el numerador.

Toca para ver más pasos...

Paso 2.1

Suma

8

$8$ y

47

$47$ .

¯ x = \frac{55 + 10 + 50 + 38 + 23 + 28 + 27 + 34 + 28}{10}

$\overline{x} = \frac{55 + 10 + 50 + 38 + 23 + 28 + 27 + 34 + 28}{10}$

Paso 2.2

Suma

55

$55$ y

10

$10$ .

¯ x = \frac{65 + 50 + 38 + 23 + 28 + 27 + 34 + 28}{10}

$\overline{x} = \frac{65 + 50 + 38 + 23 + 28 + 27 + 34 + 28}{10}$

Paso 2.3

Suma

65

$65$ y

50

$50$ .

¯ x = \frac{115 + 38 + 23 + 28 + 27 + 34 + 28}{10}

$\overline{x} = \frac{115 + 38 + 23 + 28 + 27 + 34 + 28}{10}$

Paso 2.4

Suma

115

$115$ y

38

$38$ .

¯ x = \frac{153 + 23 + 28 + 27 + 34 + 28}{10}

$\overline{x} = \frac{153 + 23 + 28 + 27 + 34 + 28}{10}$

Paso 2.5

Suma

153

$153$ y

23

$23$ .

¯ x = \frac{176 + 28 + 27 + 34 + 28}{10}

$\overline{x} = \frac{176 + 28 + 27 + 34 + 28}{10}$

Paso 2.6

Suma

176

$176$ y

28

$28$ .

¯ x = \frac{204 + 27 + 34 + 28}{10}

$\overline{x} = \frac{204 + 27 + 34 + 28}{10}$

Paso 2.7

Suma

204

$204$ y

27

$27$ .

¯ x = \frac{231 + 34 + 28}{10}

$\overline{x} = \frac{231 + 34 + 28}{10}$

Paso 2.8

Suma

231

$231$ y

34

$34$ .

¯ x = \frac{265 + 28}{10}

$\overline{x} = \frac{265 + 28}{10}$

Paso 2.9

Suma

265

$265$ y

28

$28$ .

¯ x = \frac{293}{10}

$\overline{x} = \frac{293}{10}$

¯ x = \frac{293}{10}

$\overline{x} = \frac{293}{10}$

Paso 3

Divide.

¯ x = 29.3

$\overline{x} = 29.3$

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} = n \sum i = 1 \frac{{(x_{i} - x_{a v g})}_{i}^{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.

$s = \frac{{(8 - 29.3)}^{2} + {(47 - 29.3)}^{2} + {(10 - 29.3)}^{2} + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6

Simplifica el resultado.

Toca para ver más pasos...

Paso 6.1

Simplifica el numerador.

Toca para ver más pasos...

Paso 6.1.1

Resta

$29.3$ de

$8$ .

$s = \frac{{(- 21.3)}^{2} + {(47 - 29.3)}^{2} + {(10 - 29.3)}^{2} + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.2

Eleva

$- 21.3$ a la potencia de

$2$ .

$s = \frac{453.69 + {(47 - 29.3)}^{2} + {(10 - 29.3)}^{2} + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.3

Resta

$29.3$ de

$47$ .

$s = \frac{453.69 + {17.7}^{2} + {(10 - 29.3)}^{2} + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.4

Eleva

$17.7$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + {(10 - 29.3)}^{2} + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.5

Resta

$29.3$ de

$10$ .

$s = \frac{453.69 + 313.29 + {(- 19.3)}^{2} + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.6

Eleva

$- 19.3$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + {(50 - 29.3)}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.7

Resta

$29.3$ de

$50$ .

$s = \frac{453.69 + 313.29 + 372.49 + {20.7}^{2} + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.8

Eleva

$20.7$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + {(38 - 29.3)}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.9

Resta

$29.3$ de

$38$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + {8.7}^{2} + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.10

Eleva

$8.7$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + {(23 - 29.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.11

Resta

$29.3$ de

$23$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + {(- 6.3)}^{2} + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.12

Eleva

$- 6.3$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + {(28 - 29.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.13

Resta

$29.3$ de

$28$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + {(- 1.3)}^{2} + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.14

Eleva

$- 1.3$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + {(27 - 29.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.15

Resta

$29.3$ de

$27$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + {(- 2.3)}^{2} + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.16

Eleva

$- 2.3$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + {(34 - 29.3)}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.17

Resta

$29.3$ de

$34$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + {4.7}^{2} + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.18

Eleva

$4.7$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + 22.09 + {(28 - 29.3)}^{2}}{10 - 1}$

Paso 6.1.19

Resta

$29.3$ de

$28$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + 22.09 + {(- 1.3)}^{2}}{10 - 1}$

Paso 6.1.20

Eleva

$- 1.3$ a la potencia de

$2$ .

$s = \frac{453.69 + 313.29 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.21

Suma

$453.69$ y

$313.29$ .

$s = \frac{766.98 + 372.49 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.22

Suma

$766.98$ y

$372.49$ .

$s = \frac{1139.47 + 428.49 + 75.69 + 39.69 + 1.69 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.23

Suma

$1139.47$ y

$428.49$ .

$s = \frac{1567.96 + 75.69 + 39.69 + 1.69 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.24

Suma

$1567.96$ y

$75.69$ .

$s = \frac{1643.65 + 39.69 + 1.69 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.25

Suma

$1643.65$ y

$39.69$ .

$s = \frac{1683.34 + 1.69 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.26

Suma

$1683.34$ y

$1.69$ .

$s = \frac{1685.03 + 5.29 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.27

Suma

$1685.03$ y

$5.29$ .

$s = \frac{1690.32 + 22.09 + 1.69}{10 - 1}$

Paso 6.1.28

Suma

$1690.32$ y

$22.09$ .

$s = \frac{1712.41 + 1.69}{10 - 1}$

Paso 6.1.29

Suma

$1712.41$ y

$1.69$ .

$s = \frac{1714.1}{10 - 1}$

Paso 6.2

Simplifica la expresión.

Toca para ver más pasos...

Paso 6.2.1

Resta

$1$ de

$10$ .

$s = \frac{1714.1}{9}$

Paso 6.2.2

Divide

$1714.1$ por

$9$ .

$s = 190.4\overline{5}$

Paso 7

Aproxima el resultado.

$s^{2} \approx 190.4556$