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Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute themean, median, and mode.

Question

Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute themean, median, and mode.

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Solution

Para calcular la media, la mediana y la moda de los valores de la muestra 53, 55, 70, 58, 64, 57, 53, 69, 57, 68 y 53, sigue estos pasos:

  1. Media: La media se calcula sumando todos los valores y dividiendo por el número total de valores. Media=53+55+70+58+64+57+53+69+57+68+5311 \text{Media} = \frac{53 + 55 + 70 + 58 + 64 + 57 + 53 + 69 + 57 + 68 + 53}{11} Media=6571159.73 \text{Media} = \frac{657}{11} \approx 59.73

  2. Mediana: La mediana es el valor medio cuando los datos están ordenados de menor a mayor. Primero, ordenamos los datos: 53,53,53,55,57,57,58,64,68,69,70 53, 53, 53, 55, 57, 57, 58, 64, 68, 69, 70 Como hay 11 valores, la mediana es el sexto valor en la lista ordenada. Mediana=57 \text{Mediana} = 57

  3. Moda: La moda es el valor que aparece con mayor frecuencia en el conjunto de datos. Observamos que el valor 53 aparece tres veces, más que cualquier otro valor. Moda=53 \text{Moda} = 53

Por lo tanto, la media es aproximadamente 59.73, la mediana es 57 y la moda es 53.

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