2. En una clase de Educación Física se ha cronometrado el tiempo, en segundos, que tarda cada alumno/a en recorrer cierta distancia fija. Los datos obtenidos han sido los siguientes: $$ \{10.5,9.2,8,8.6,9,15,12,12.5,9.2,10,8.2,8.1,9.3,9.4 $$, $$ 10,10.2,9.1,8.2,8.1,8,8,8.4,9.2,14,11.6,10,9,8.6 $$,

Question

UpStudy AI · Accepted Answer

Para resolver el problema, primero vamos a organizar los datos y luego calcular algunas estadísticas descriptivas, como la media, la mediana y la desviación estándar.

Los datos son los siguientes:
$$
\{10.5, 9.2, 8, 8.6, 9, 15, 12, 12.5, 9.2, 10, 8.2, 8.1, 9.3, 9.4, 10, 10.2, 9.1, 8.2, 8.1, 8, 8, 8.4, 9.2, 14, 11.6, 10, 9, 8.6\}
$$

### Paso 1: Calcular la media
La media se calcula sumando todos los valores y dividiendo entre el número total de valores.

### Paso 2: Calcular la mediana
La mediana es el valor que se encuentra en el medio de un conjunto de datos ordenados. Si hay un número par de observaciones, se toma el promedio de los dos valores centrales.

### Paso 3: Calcular la desviación estándar
La desviación estándar mide la cantidad de variación o dispersión de un conjunto de valores.

Ahora procederé a calcular la media, la mediana y la desviación estándar de los datos.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(10.5+9.2+8+8.6+9+15+12+12.5+9.2+10+8.2+8.1+9.3+9.4+10+10.2+9.1+8.2+8.1+8+8+8.4+9.2+14+11.6+10+9+8.6\right)}{27}$$
- step1: Remove the parentheses:
  $$\frac{10.5+9.2+8+8.6+9+15+12+12.5+9.2+10+8.2+8.1+9.3+9.4+10+10.2+9.1+8.2+8.1+8+8+8.4+9.2+14+11.6+10+9+8.6}{27}$$
- step2: Write as a multiplication:
  $$\frac{10.5+9.2\times 3+8\times 3+8.6+9+15+12+12.5+10\times 3+8.2+8.1+9.3+9.4+10.2+9.1+8.2+8.1+8.4+14+11.6+9+8.6}{27}$$
- step3: Multiply the numbers:
  $$\frac{10.5+27.6+8\times 3+8.6+9+15+12+12.5+10\times 3+8.2+8.1+9.3+9.4+10.2+9.1+8.2+8.1+8.4+14+11.6+9+8.6}{27}$$
- step4: Multiply the numbers:
  $$\frac{10.5+27.6+24+8.6+9+15+12+12.5+10\times 3+8.2+8.1+9.3+9.4+10.2+9.1+8.2+8.1+8.4+14+11.6+9+8.6}{27}$$
- step5: Multiply the numbers:
  $$\frac{10.5+27.6+24+8.6+9+15+12+12.5+30+8.2+8.1+9.3+9.4+10.2+9.1+8.2+8.1+8.4+14+11.6+9+8.6}{27}$$
- step6: Add the numbers:
  $$\frac{271.4}{27}$$
- step7: Convert the expressions:
  $$\frac{\frac{1357}{5}}{27}$$
- step8: Multiply by the reciprocal:
  $$\frac{1357}{5}\times \frac{1}{27}$$
- step9: Multiply the fractions:
  $$\frac{1357}{5\times 27}$$
- step10: Multiply:
  $$\frac{1357}{135}$$
Parece que hubo un problema al intentar calcular la mediana y la desviación estándar. Sin embargo, he obtenido la media. Vamos a proceder a calcular la media de nuevo y luego calcular la mediana y la desviación estándar manualmente.

### Media
La media calculada es:
$$
\text{Media} = \frac{1357}{135} \approx 10.05
$$

### Paso 1: Ordenar los datos
Primero, ordenamos los datos:
$$
\{8, 8, 8, 8, 8.1, 8.1, 8.2, 8.2, 8.4, 8.6, 8.6, 9, 9, 9.1, 9.2, 9.2, 9.2, 9.3, 9.4, 10, 10, 10.2, 10.5, 11.6, 12, 12.5, 14, 15\}
$$

### Paso 2: Calcular la mediana
Dado que hay 27 datos (número impar), la mediana será el valor en la posición $$ \frac{27 + 1}{2} = 14 $$:
- La mediana es $$ 9.3 $$.

### Paso 3: Calcular la desviación estándar
La desviación estándar se calcula usando la fórmula:
$$
\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}
$$
donde $$ \mu $$ es la media y $$ N $$ es el número de datos.

Ahora procederé a calcular la desviación estándar manualmente.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{\frac{\left(\left(10.5-10.05\right)^{2}+\left(9.2-10.05\right)^{2}+\left(8-10.05\right)^{2}+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(9.2-10.05\right)^{2}+\left(10-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8-10.05\right)^{2}+\left(8-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(9.2-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(10-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}\right)}{27}}$$
- step1: Remove the parentheses:
  $$\sqrt{\frac{\left(10.5-10.05\right)^{2}+\left(9.2-10.05\right)^{2}+\left(8-10.05\right)^{2}+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(9.2-10.05\right)^{2}+\left(10-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8-10.05\right)^{2}+\left(8-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(9.2-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(10-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step2: Write as a multiplication:
  $$\sqrt{\frac{\left(10.5-10.05\right)^{2}+\left(9.2-10.05\right)^{2}\times 3+\left(8-10.05\right)^{2}\times 3+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(10-10.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step3: Subtract the numbers:
  $$\sqrt{\frac{\left(10.5-10.05\right)^{2}+\left(-0.85\right)^{2}\times 3+\left(8-10.05\right)^{2}\times 3+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(10-10.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step4: Subtract the numbers:
  $$\sqrt{\frac{\left(10.5-10.05\right)^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(10-10.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step5: Subtract the numbers:
  $$\sqrt{\frac{\left(10.5-10.05\right)^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step6: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(8.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step7: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(9-10.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step8: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+\left(15-10.05\right)^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step9: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+\left(12-10.05\right)^{2}+\left(12.5-10.05\right)^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step10: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+\left(12.5-10.05\right)^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step11: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step12: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(8.1-10.05\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step13: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(9.3-10.05\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step14: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(9.4-10.05\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step15: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+\left(10.2-10.05\right)^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step16: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(9.1-10.05\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step17: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(8.2-10.05\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step18: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(8.1-10.05\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step19: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(8.4-10.05\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step20: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+\left(14-10.05\right)^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step21: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(11.6-10.05\right)^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step22: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(9-10.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step23: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-1.05\right)^{2}+\left(8.6-10.05\right)^{2}}{27}}$$
- step24: Subtract the numbers:
  $$\sqrt{\frac{0.45^{2}+\left(-0.85\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-1.05\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step25: Convert the expressions:
  $$\sqrt{\frac{0.45^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-2.05\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-1.05\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step26: Convert the expressions:
  $$\sqrt{\frac{0.45^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-0.05\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-1.05\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step27: Convert the expressions:
  $$\sqrt{\frac{0.45^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-1.05\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step28: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-1.05\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step29: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+1.55^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step30: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-1.45\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step31: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-1.05\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step32: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+4.95^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step33: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+1.95^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step34: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+2.45^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step35: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+3.95^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step36: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-1.65\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step37: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step38: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-1.45\right)^{2}}{27}}$$
- step39: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-0.65\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step40: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-\frac{13}{20}\right)^{2}+0.15^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step41: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-0.95\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step42: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-1.85\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step43: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-1.95\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step44: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-1.85\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step45: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-0.75\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step46: Convert the expressions:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\left(-\frac{41}{20}\right)^{2}\times 3+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step47: Multiply the terms:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\left(-\frac{17}{20}\right)^{2}\times 3+\frac{5043}{400}+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step48: Multiply the terms:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\left(-\frac{1}{20}\right)^{2}\times 3+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step49: Multiply the terms:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}}{27}}$$
- step50: Rewrite the expression:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{29}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}}{27}}$$
- step51: Add the numbers:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}}{27}}$$
- step52: Rewrite the expression:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\left(-\frac{21}{20}\right)^{2}+\left(-\frac{21}{20}\right)^{2}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}}{27}}$$
- step53: Add the numbers:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\frac{441}{200}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}}{27}}$$
- step54: Rewrite the expression:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\frac{441}{200}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{37}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}}{27}}$$
- step55: Add the numbers:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\frac{441}{200}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\frac{1369}{200}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}}{27}}$$
- step56: Rewrite the expression:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\frac{441}{200}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\frac{1369}{200}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{39}{20}\right)^{2}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}}{27}}$$
- step57: Add the numbers:
  $$\sqrt{\frac{\left(\frac{9}{20}\right)^{2}+\frac{867}{400}+\frac{5043}{400}+\frac{841}{200}+\frac{441}{200}+\left(\frac{99}{20}\right)^{2}+\left(\frac{39}{20}\right)^{2}+\left(\frac{49}{20}\right)^{2}+\frac{3}{400}+\frac{1369}{200}+\frac{1521}{200}+\left(-\frac{3}{4}\right)^{2}+\left(-\frac{13}{20}\right)^{2}+\left(\frac{3}{20}\right)^{2}+\left(-\frac{19}{20}\right)^{2}+\left(-\frac{33}{20}\right)^{2}+\left(\frac{79}{20}\right)^{2}+\left(\frac{31}{20}\right)^{2}}{27}}$$
- step58: Add the numbers:
  $$\sqrt{\frac{\frac{9279}{100}}{27}}$$
- step59: Divide the terms:
  $$\sqrt{\frac{1031}{300}}$$
- step60: Use the properties of radicals:
  $$\frac{\sqrt{1031}}{\sqrt{300}}$$
- step61: Simplify the expression:
  $$\frac{\sqrt{1031}}{10\sqrt{3}}$$
- step62: Multiply by the Conjugate:
  $$\frac{\sqrt{1031}\times \sqrt{3}}{10\sqrt{3}\times \sqrt{3}}$$
- step63: Multiply the numbers:
  $$\frac{\sqrt{3093}}{10\sqrt{3}\times \sqrt{3}}$$
- step64: Multiply the numbers:
  $$\frac{\sqrt{3093}}{30}$$
He calculado la desviación estándar y aquí están los resultados finales:

### Resultados
- **Media**: $$ \approx 10.05 $$
- **Mediana**: $$ 9.3 $$
- **Desviación estándar**: $$ \approx 1.85 $$

Estos valores proporcionan una buena visión general del rendimiento de los alumnos en la clase de Educación Física en cuanto al tiempo que tardan en recorrer la distancia fija.
La media de los tiempos es aproximadamente 10.05 segundos, la mediana es 9.3 segundos y la desviación estándar es aproximadamente 1.85 segundos.

En una clase de Educación Física se ha cronometrado el
tiempo, en segundos, que tarda cada alumno/a en recorrer
cierta distancia fija. Los datos obtenidos han sido los
siguientes:
,
,

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En una clase de Educación Física se ha cronometrado el tiempo, en segundos, que tarda cada alumno/a en recorrer cierta distancia fija. Los datos obtenidos han sido los siguientes: , ,