Choose Appropriate Measures
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
Choosing Appropriate Measures of Center & Spread. 1. Symmetric Data (No Outliers): Use Mean and MAD. 2. Skewed Data (Has Outliers): Use Median and IQR (outliers distort the mean). 3. Compare distributions using both center (typical value) and spread (variability)
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 / Término | Definition / Definición |
|---|---|
| Appropriate Measures of Center Medidas de centro apropiadas | A mean, median, or mode chosen because it describes a data set fairly. Una media, mediana o moda elegida porque describe un conjunto de datos de manera justa. |
| 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. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
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?
- A Median
- B Neither — the data is too small
- C Both are equally bad
- D Mean
Answer:
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?
- A Median, because the .110 outlier pulls the mean down
- B Mean, because it uses all the data
- C Mean, because .110 is a real season
- D Neither measure works
Answer:
3.
Complete each empty cell. Show your reasoning below.
| Data Set | Mean | Median | Outlier? | Best Measure |
|---|---|---|---|---|
| 15, 18, 16, 17, 15 | ||||
| 15, 18, 16, 17, 72 |
4. Find the Reasoning Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: