Comparing Center and Spread
Aligned to S-ID.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
To compare data sets, look at center (mean or median) for a typical value and spread (range or IQR) for how much the values vary. Similar centers can hide very different spreads.
Worked examples
Example 1
Data set A is 4, 5, 6 and set B is 1, 5, 9. Both have mean 5, but A's range is 6 − 4 = 2 while B's range is 9 − 1 = 8, so B is far more spread out.
Example 2
Standard deviation beats range for spread, because range depends only on the two extreme values.
Example 3
Report centre and spread together. A mean with no spread hides whether the group is tight or scattered, and the decision often turns on that.
Practice questions
- Find the mean of 3, 7, 8, 10, 12.
- Two classes both average 80. What else should you compare, and why?
- Find the range of 15, 22, 22, 30, 41.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Comparar Centro y Dispersión
Para comparar conjuntos de datos, mira el centro (media o mediana) para un valor típico y la dispersión (rango o RIC) para cuánto varían los valores. Centros parecidos pueden ocultar dispersiones muy distintas.
Ejemplo 1: El conjunto A es 4, 5, 6 y el conjunto B es 1, 5, 9. Ambos tienen media 5, pero el rango de A es 6 − 4 = 2 mientras que el de B es 9 − 1 = 8, así que B está mucho más disperso.
Ejemplo 2: La desviación estándar vence al rango para la dispersión, porque el rango depende solo de los dos valores extremos.
Ejemplo 3: Reporta centro y dispersión juntos. Una media sin dispersión esconde si el grupo es cerrado o disperso, y muchas veces de eso depende la decisión.
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