Appropriate Measures

6.DS.6d · Unit 8 · Lesson 4

Name   Period

Objectives / Objetivos

Content Objective: I can choose the best measure of center for a data set based on its shape.

Language Objective: I can explain my choice using the words mean, median, outlier, and skewed.

Key Idea / Idea clave

Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical.

I Notice / Observo

  • How does the 58-point game compare to the other scores?
  • What is the mean? What is the median?

I Wonder / Me pregunto

  • When does an outlier make the mean misleading?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Mean
Media		The average. Add all the numbers, then divide by how many there are.
El promedio. Suma todos los números y divide entre cuántos hay.
Median
Mediana		The middle number when you put them in order.
El número del medio cuando los pones en orden.
Outlier
Valor atípico		A number that is much bigger or smaller than the rest.
Un número mucho mayor o menor que los demás.
Skewed
Sesgado		When most data sits on one side with a tail on the other.
Cuando la mayoría de los datos está de un lado con una cola del otro.
Data distribution
Distribución de datos		How the data looks: where it sits and how spread out it is.
Cómo se ven los datos: dónde están y qué tan separados están.
Variability
Variabilidad		How spread out the numbers are.
Qué tan separados están los números.

Practice Preview / Vista previa de práctica

  1. A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?
    1. Mean
    2. Median
    3. Neither — the data is too small
    4. Both are equally bad
  2. A baseball player's batting averages over 6 seasons are: .280, .295, .290, .285, .300, .110. The .110 was an injury-shortened season. Which measure better represents the player's typical batting average?
    1. Median, because the .110 outlier pulls the mean down
    2. Mean, because it uses all the data
    3. Mean, because .110 is a real season
    4. Neither measure works
  3. Problem 3
  4. Find the Reasoning Error
    1. Step 1: Data — Player minutes per game: 32, 34, 30, 35, 33, 5
    2. Step 2: Find mean — Sum = 169, Count = 6, Mean = 28.2
    3. Step 3: Find median — Ordered: 5, 30, 32, 33, 34, 35 → Median = (32+33) ÷ 2 = 32.5
    4. Step 4: Conclusion — The mean (28.2) is the best measure because it uses all the data.

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: