Averages, and which to use · Promedios, y cuáles usar
| English | Español |
|---|---|
| mean/miːn/ | media |
| median/ˈmiːdiːən/ | mediana |
| mode/məʊd/ | moda |
| symmetric/sɪˈmetrɪk/ | simétrica |
| skewed/skjuːd/ | sesgada |
A centre answers a specified question
- The · El mean · media 平均数 measures total per observation; the median · mediana 中位数 locates the ordered middle; the mode · moda 众数 identifies a most frequent value.
- No single summary answers every question. A mode can describe a category, while mean and median need a suitable numerical or ordered scale.
Combine totals before combining groups
- Compute the mean as $\bar x=\sum x/n$, or $\sum fx/\sum f$ for exact-value frequency data. For an even count, the numerical median averages the middle two ordered values.
- To combine group means, weight them by group size. Ten scores with mean 60 and twenty with mean 75 have combined mean 70, not 67.5.
Which average can be used for favourite subject? · ¿Qué promedio se puede usar para la materia favorita?
Categories cannot be added or ordered meaningfully, so only the most frequent value applies. · Las categorías no se pueden sumar ni ordenar de manera significativa, por lo que solo aplica el valor más frecuente.
Interpret shape without inventing observations
- A symmetric 对称 distribution need not have its mode at the centre if it has two peaks. Do not assume mean, median and mode always coincide.
- A skewed 偏态 pattern or extreme values can separate the mean from the median. Inspect the supplied data rather than treating one gap between summaries as a complete shape description.
A mean much larger than the median suggests a few unusually large values. · Una media mucho mayor que la mediana sugiere unos pocos valores inusualmente grandes.
A mean well above the median can suggest high extreme values or a right-skewed pattern. It does not uniquely determine the full data shape; inspect the observations. · Una media muy por encima de la mediana puede sugerir valores extremos altos o un patrón sesgado a la derecha. No determina únicamente la forma completa de los datos; inspecciona las observaciones.
Nine incomes of 30000 and one of 150000. The mean is $\bar x=[9(30000)+150000]/10=42000$, while median is 30000. The mean correctly describes total income per person; it does not claim anybody earns 42000. The median identifies the ordered middle.
Nine people earn 30000 and one earns 150000. What is the median? · Nueve personas ganan 30000 y una gana 150000. ¿Cuál es la mediana?
Ordered, the middle values are both 30000. The single large value does not move it. · Ordenados, los valores centrales son ambos 30000. El único valor grande no lo desplaza.
Which average best describes a typical income in that group? · ¿Qué promedio describe mejor un ingreso típico en ese grupo?
In this supplied group, nine of ten incomes equal the median 30000. The mean 42000 is still a valid total-per-person summary, but is not what most individuals earn. · En este grupo proporcionado, nueve de diez ingresos son iguales a la mediana 30000. La media 42000 sigue siendo un resumen válido de total por persona, pero no es lo que gana la mayoría de los individuos.
Explain what your summary represents. In the supplied income example the median also equals what nine people earn. That particular fact comes from the actual list, not from a general definition of median. Sheet 2.6 compares weighted means and the effect of a changed extreme.
A grouped frequency table with numeric intervals usually loses individual values. Using class midpoints gives an estimated mean unless further information makes it exact. Do not confuse interval groups with a frequency table of exact distinct values, whose mean can be calculated exactly.
What can generally be calculated from a grouped frequency table of numeric intervals when the individual values are not supplied? · ¿Qué puede calcularse generalmente a partir de una tabla de frecuencias agrupadas de intervalos numéricos cuando no se proporcionan los valores individuales?
Class midpoints give an estimated mean unless additional information makes it exact. A table of exact distinct values and their frequencies is different and permits an exact mean. · Los puntos medios de clase dan una media estimada a menos que información adicional la haga exacta. Una tabla de valores distintos exactos y sus frecuencias es diferente y permite una media exacta.