Aprende las formulas para la media, la mediana y la moda con ejemplos resueltos, y descubre cuando usar cada medida de tendencia central.
La tendencia central es un concepto estadistico que identifica un valor unico que representa el "centro" o "valor tipico" de un conjunto de datos. Las tres medidas mas comunes de tendencia central son la media, la mediana y la moda. Cada medida responde la misma pregunta de forma diferente: "¿Cual es un valor tipico en estos datos?" Elegir la correcta depende de la forma de tus datos y la pregunta que intentas responder.
donde n = numero de valores en el conjunto de datos
donde f es la frecuencia (conteo) de cada valor en el conjunto de datos
| Caracteristica | Media | Mediana | Moda |
|---|---|---|---|
| Definicion | Suma dividida por conteo | Valor central al ordenar | Valor mas frecuente |
| Afectada por valores atipicos | Si, mucho | No | No |
| Mejor para | Datos simetricos | Datos sesgados | Datos categoricos |
| ¿Siempre unica? | Si | Si | No, puede tener 0, 1 o varias |
| ¿Funciona con datos no numericos? | No | No | Si |
| ¿Facil de calcular? | Si, aritmetica simple | Requiere ordenar primero | Requiere contar frecuencias |
| Uso comun en el mundo real | Salario promedio, GPA | Precio mediano de vivienda | Producto mas popular |
Usar Media -> Datos simetricos, sin valores atipicos (p. ej., puntajes de examenes, ingresos promedio)
Usar Mediana -> Datos sesgados o con valores atipicos (p. ej., precios de vivienda, ingresos)
Usar Moda -> Datos categoricos o encontrar lo mas comun (p. ej., producto popular)In everyday language, "average" and "mean" are used interchangeably. Technically, "average" can refer to any measure of central tendency (mean, median, or mode), but the arithmetic mean is the most common type. When someone says "average," they almost always mean the arithmetic mean.
Yes. If every value in a dataset appears exactly once (for example, 3, 7, 12, 18), then no value repeats and the dataset has no mode.
Income data is typically right-skewed because a small number of very high earners pull the mean upward. For instance, if 9 people earn $50,000 and 1 person earns $5,000,000, the mean is $545,000 but the median is $50,000. The median more accurately represents the typical earner.
Sort the numbers in ascending order, then take the two middle values and calculate their average. For example, in the sorted set 2, 4, 6, 8, the two middle values are 4 and 6 so the median is (4 + 6) / 2 = 5.
A bimodal dataset has two values that appear with equal highest frequency. For example, in the set 1, 2, 2, 5, 5, 7, both 2 and 5 appear twice. Bimodal distributions often indicate that the data comes from two distinct groups mixed together.
Yes, and they often are. In a perfectly symmetric distribution (like a bell curve), all three are equal. In a skewed distribution, they diverge. For example, in the set 1, 2, 2, 3, 10, the mode is 2, the median is 2, and the mean is 3.6.
