Matemática básica Ejemplos

$13$ , $18$ , $27$ , $19$ , $14$ , $31$ , $8$ , $17$ , $23$ , $8$ , $17$ , $23$ , $20$ , $24$ , $23$ , $19$ , $27$ , $40$ , $13$ , $23$

Paso 1

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

$\overline{x} = \frac{13 + 18 + 27 + 19 + 14 + 31 + 8 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2

Simplifica el numerador.

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Paso 2.1

Suma $13$ y $18$ .

$\overline{x} = \frac{31 + 27 + 19 + 14 + 31 + 8 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.2

Suma $31$ y $27$ .

$\overline{x} = \frac{58 + 19 + 14 + 31 + 8 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.3

Suma $58$ y $19$ .

$\overline{x} = \frac{77 + 14 + 31 + 8 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.4

Suma $77$ y $14$ .

$\overline{x} = \frac{91 + 31 + 8 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.5

Suma $91$ y $31$ .

$\overline{x} = \frac{122 + 8 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.6

Suma $122$ y $8$ .

$\overline{x} = \frac{130 + 17 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.7

Suma $130$ y $17$ .

$\overline{x} = \frac{147 + 23 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.8

Suma $147$ y $23$ .

$\overline{x} = \frac{170 + 8 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.9

Suma $170$ y $8$ .

$\overline{x} = \frac{178 + 17 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.10

Suma $178$ y $17$ .

$\overline{x} = \frac{195 + 23 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.11

Suma $195$ y $23$ .

$\overline{x} = \frac{218 + 20 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.12

Suma $218$ y $20$ .

$\overline{x} = \frac{238 + 24 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.13

Suma $238$ y $24$ .

$\overline{x} = \frac{262 + 23 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.14

Suma $262$ y $23$ .

$\overline{x} = \frac{285 + 19 + 27 + 40 + 13 + 23}{20}$

Paso 2.15

Suma $285$ y $19$ .

$\overline{x} = \frac{304 + 27 + 40 + 13 + 23}{20}$

Paso 2.16

Suma $304$ y $27$ .

$\overline{x} = \frac{331 + 40 + 13 + 23}{20}$

Paso 2.17

Suma $331$ y $40$ .

$\overline{x} = \frac{371 + 13 + 23}{20}$

Paso 2.18

Suma $371$ y $13$ .

$\overline{x} = \frac{384 + 23}{20}$

Paso 2.19

Suma $384$ y $23$ .

$\overline{x} = \frac{407}{20}$

Paso 3

Divide.

$\overline{x} = 20.35$

Paso 4

La media debería redondearse a una cifra decimal más que los datos originales. Si los datos originales fueran mixtos, redondea a una cifra decimal más que el dato menos preciso.

$\overline{x} = 20.4$

Paso 5

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

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

Paso 6

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

$s = \frac{{(13 - 20.4)}^{2} + {(18 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7

Simplifica el resultado.

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Paso 7.1

Simplifica el numerador.

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Paso 7.1.1

Resta $20.4$ de $13$ .

$s = \frac{{(- 7.4)}^{2} + {(18 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.2

Eleva $- 7.4$ a la potencia de $2$ .

$s = \frac{54.76 + {(18 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.3

Resta $20.4$ de $18$ .

$s = \frac{54.76 + {(- 2.4)}^{2} + {(27 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.4

Eleva $- 2.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + {(27 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.5

Resta $20.4$ de $27$ .

$s = \frac{54.76 + 5.76 + {6.6}^{2} + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.6

Eleva $6.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + {(19 - 20.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.7

Resta $20.4$ de $19$ .

$s = \frac{54.76 + 5.76 + 43.56 + {(- 1.4)}^{2} + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.8

Eleva $- 1.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + {(14 - 20.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.9

Resta $20.4$ de $14$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + {(- 6.4)}^{2} + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.10

Eleva $- 6.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + {(31 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.11

Resta $20.4$ de $31$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + {10.6}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.12

Eleva $10.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.13

Resta $20.4$ de $8$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + {(- 12.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.14

Eleva $- 12.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.15

Resta $20.4$ de $17$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + {(- 3.4)}^{2} + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.16

Eleva $- 3.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + {(23 - 20.4)}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.17

Resta $20.4$ de $23$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + {2.6}^{2} + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.18

Eleva $2.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + {(8 - 20.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.19

Resta $20.4$ de $8$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + {(- 12.4)}^{2} + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.20

Eleva $- 12.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + {(17 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.21

Resta $20.4$ de $17$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + {(- 3.4)}^{2} + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.22

Eleva $- 3.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + {(23 - 20.4)}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.23

Resta $20.4$ de $23$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + {2.6}^{2} + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.24

Eleva $2.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + {(20 - 20.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.25

Resta $20.4$ de $20$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + {(- 0.4)}^{2} + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.26

Eleva $- 0.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + {(24 - 20.4)}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.27

Resta $20.4$ de $24$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + {3.6}^{2} + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.28

Eleva $3.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + {(23 - 20.4)}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.29

Resta $20.4$ de $23$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + {2.6}^{2} + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.30

Eleva $2.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + {(19 - 20.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.31

Resta $20.4$ de $19$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + {(- 1.4)}^{2} + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.32

Eleva $- 1.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + {(27 - 20.4)}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.33

Resta $20.4$ de $27$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + {6.6}^{2} + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.34

Eleva $6.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + {(40 - 20.4)}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.35

Resta $20.4$ de $40$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + {19.6}^{2} + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.36

Eleva $19.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + {(13 - 20.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.37

Resta $20.4$ de $13$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + {(- 7.4)}^{2} + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.38

Eleva $- 7.4$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + {(23 - 20.4)}^{2}}{20 - 1}$

Paso 7.1.39

Resta $20.4$ de $23$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + {2.6}^{2}}{20 - 1}$

Paso 7.1.40

Eleva $2.6$ a la potencia de $2$ .

$s = \frac{54.76 + 5.76 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.41

Suma $54.76$ y $5.76$ .

$s = \frac{60.52 + 43.56 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.42

Suma $60.52$ y $43.56$ .

$s = \frac{104.08 + 1.96 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.43

Suma $104.08$ y $1.96$ .

$s = \frac{106.04 + 40.96 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.44

Suma $106.04$ y $40.96$ .

$s = \frac{147 + 112.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.45

Suma $147$ y $112.36$ .

$s = \frac{259.36 + 153.76 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.46

Suma $259.36$ y $153.76$ .

$s = \frac{413.12 + 11.56 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.47

Suma $413.12$ y $11.56$ .

$s = \frac{424.68 + 6.76 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.48

Suma $424.68$ y $6.76$ .

$s = \frac{431.44 + 153.76 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.49

Suma $431.44$ y $153.76$ .

$s = \frac{585.2 + 11.56 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.50

Suma $585.2$ y $11.56$ .

$s = \frac{596.76 + 6.76 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.51

Suma $596.76$ y $6.76$ .

$s = \frac{603.52 + 0.16 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.52

Suma $603.52$ y $0.16$ .

$s = \frac{603.68 + 12.96 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.53

Suma $603.68$ y $12.96$ .

$s = \frac{616.64 + 6.76 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.54

Suma $616.64$ y $6.76$ .

$s = \frac{623.4 + 1.96 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.55

Suma $623.4$ y $1.96$ .

$s = \frac{625.36 + 43.56 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.56

Suma $625.36$ y $43.56$ .

$s = \frac{668.92 + 384.16 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.57

Suma $668.92$ y $384.16$ .

$s = \frac{1053.08 + 54.76 + 6.76}{20 - 1}$

Paso 7.1.58

Suma $1053.08$ y $54.76$ .

$s = \frac{1107.84 + 6.76}{20 - 1}$

Paso 7.1.59

Suma $1107.84$ y $6.76$ .

$s = \frac{1114.6}{20 - 1}$

Paso 7.2

Simplifica la expresión.

Toca para ver más pasos...

Paso 7.2.1

Resta $1$ de $20$ .

$s = \frac{1114.6}{19}$

Paso 7.2.2

Divide $1114.6$ por $19$ .

$s = 58.66315789$

Paso 8

Aproxima el resultado.

$s^{2} \approx 58.6632$