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Center, Spread, and Shape

  • Grade 6
  • Mathematics
  • 6.SP.A.2
  • Statistics & Probability
  • Free lesson

Aligned to 6.SP.A.2 — Common Core State Standards for Mathematics.

What this lesson teaches

A data set is described three ways: its center (a typical value like the mean or median), its spread (how far the values stretch), and its shape (are values bunched, even, or skewed?).

Worked examples

Example 1

For test scores 80, 82, 85, 88, 90: the center (median) is 85, the spread (range) is 90 − 80 = 10, and the shape is fairly even with no big gaps.

Example 2

For 10, 12, 12, 13, 40: the median is 12 and the range is 30, but that 40 is an outlier stretching the spread far past where most values sit.

Example 3

Shape matters. Scores clustered at the top with a long tail down look very different from scores spread evenly, even with the same mean.

Practice questions

  1. Find the median (center) of 4, 7, 9, 12, 15.
  2. Find the range (spread) of 20, 22, 30, 45.
  3. Describe the shape of a data set where most values cluster low with one very high value.

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.

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En español

Centro, Dispersión y Forma

Un conjunto de datos se describe de tres maneras: su centro (un valor típico como la media o la mediana), su dispersión (qué tanto se extienden los valores) y su forma (¿están agrupados, parejos o sesgados?).

Ejemplo 1: Para las calificaciones 80, 82, 85, 88, 90: el centro (mediana) es 85, la dispersión (rango) es 90 − 80 = 10, y la forma es bastante pareja sin grandes huecos.

Ejemplo 2: Para 10, 12, 12, 13, 40: la mediana es 12 y el rango es 30, pero ese 40 es un valor atípico que estira la dispersión mucho más allá de donde está la mayoría.

Ejemplo 3: La forma importa. Calificaciones agrupadas arriba con una cola larga hacia abajo se ven muy distintas de calificaciones parejas, aun con la misma media.

More Statistics & Probability lessons

Statistical Variability and Data Displays6.SP.A.3What Makes a Statistical Question6.SP.A.1Dot Plots, Histograms, and Box Plots6.SP.B.4Summarizing a Data Set6.SP.B.5

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