Comparing Populations with Center & Spread
Aligned to 7.SP.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
Compare two populations using a measure of center (mean or median) and a measure of variability (range, IQR, or MAD). The center compares typical values; the variability compares how consistent the data are.
Worked examples
Example 1
Shop A's wait times: mean 8 min, MAD 1 min. Shop B: mean 8 min, MAD 4 min. The typical wait is the same, but Shop A is far more consistent because its MAD is smaller.
Example 2
Farm A's tomato weights: mean 120 g, MAD 5 g. Farm B: mean 135 g, MAD 6 g. B's tomatoes are typically heavier and just as consistent.
Example 3
Report both numbers. A mean with no spread hides whether the group is tight or scattered, and the spread is often what the decision turns on.
Practice questions
- Data set X has median 12 and IQR 3; set Y has median 12 and IQR 9. Which is more spread out?
- Two teams both average 20 points. Team 1's range is 5, Team 2's is 25. Which is more consistent?
- Name one measure of center and one measure of variability you would report to compare two classes' test scores.
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 Poblaciones con Centro y Dispersión
Compara dos poblaciones usando una medida de centro (media o mediana) y una medida de variabilidad (rango, RIC o DMA). El centro compara los valores típicos; la variabilidad compara qué tan consistentes son los datos.
Ejemplo 1: Tiempos de espera de la Tienda A: media 8 min, DMA 1 min. Tienda B: media 8 min, DMA 4 min. La espera típica es igual, pero la Tienda A es mucho más consistente porque su DMA es menor.
Ejemplo 2: Peso de los tomates de la Granja A: media 120 g, DMA 5 g. Granja B: media 135 g, DMA 6 g. Los de B son típicamente más pesados e igual de consistentes.
Ejemplo 3: Reporta los dos números. Una media sin dispersión esconde si el grupo es cerrado o disperso, y muchas veces la decisión depende de la dispersión.
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