Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 2, Lesson 10: Choose Appropriate Measures

Standard 6.DS.6d

What students are learning Qué aprenden

Key idea: If the data has no outliers (numbers far from the rest), use the mean and the mean absolute deviation (MAD) to describe it. If the data has outliers or leans to one side, use the median and the interquartile range (IQR), because an outlier pulls the mean away from most of the numbers. To compare two data sets, look at both the typical value and the spread.Idea clave: Si los datos no tienen valores atípicos (números muy lejos del resto), usa la media y la desviación media absoluta para describirlos. Si los datos tienen valores atípicos o están cargados hacia un lado, usa la mediana y el rango intercuartílico, porque un valor atípico jala la media lejos de la mayoría de los números. Para comparar dos conjuntos de datos, mira tanto el valor típico como la dispersión.

Words to know Palabras clave

Appropriate Measures of Center Medidas de centro apropiadas
The mean, median, or mode that best fits the data.
La media, mediana o moda que mejor describe los datos.
Mean Media
Add all the numbers, then divide by how many.
Suma todos los números y divide entre cuántos hay.
Median Mediana
The middle number when they are in order.
El número del medio cuando están en orden.
Outlier Valor atípico
A number far bigger or smaller than the rest.
Un número mucho mayor o menor que los demás.
Skewed Sesgado
Most data sits on one side, with a tail on the other.
La mayoría de los datos está de un lado, con una cola del otro.
Data distribution Distribución de datos
Where the values sit and how far apart they are.
Dónde están los valores y qué tan separados están.
Variability Variabilidad
How far apart the numbers are.
Qué tan separados están los números.
Cluster Agrupamiento
Values that are near each other.
Valores que están cerca unos de otros.
Gap Brecha
An empty space where there is no data.
Un espacio vacío donde no hay datos.

Sentence starters Frases para empezar

I know ___ because ___.

First, I ___. Then, I ___.

The answer is ___, so ___.

How we did it in class today Cómo lo hicimos hoy en clase

  1. My data, the top scorer's points: 22, 24, 20, 25, 23, 21, 58. I notice 58 is much bigger than the rest, so it is an outlier.
  2. Mean: 22 + 24 + 20 + 25 + 23 + 21 + 58 = 193, then 193 ÷ 7 ≈ 27.6.
  3. Median: in order they are 20, 21, 22, 23, 24, 25, 58. The middle (4th) value is 23.
  4. The mean (27.6) is higher than 6 of the 7 games because 58 pulled it up. So the median (23) better shows a typical game.

Play with today's math Jueguen con las matemáticas

Interactive Lesson Model — This is the exact same interactive tool your student used in class today. Change the numbers and watch what happens!

Modelo interactivo de la lección — Esta es la misma herramienta interactiva que su estudiante usó en clase hoy. ¡Cambie los números y observe qué sucede!

Works on a phone, a tablet, or a computer. Nothing to install, nothing to sign in to.

Try this together Inténtenlo juntos

Pick one question to talk about. You don't need to do them all!

Six friends timed their trips to school in minutes: 12, 10, 14, 11, 13, 60. Which measure should they use to describe a typical trip time?

  1. Mean, because it uses all values
  2. Median, because 60 is an outlier
  3. Neither works for this data
  4. Mean, because it is always best
Check the answer

The answer is: Median, because 60 is an outlier

Take-home sheet Hoja para llevar a casa

Lesson 2.10: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 2.10: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

If they get stuck... Si se traban...

Watch out for this: A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.

Try asking: "Can you show me how you got that? Did we miss a step?"
Pregunte: «¿Puedes mostrarme cómo lo hiciste? ¿Nos saltamos algún paso?» Hablar de las matemáticas en voz alta ayuda mucho.

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