Describe Data Using the Mean
Name Period
Objectives / Objetivos
Content Objective: I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.
Language Objective: I can explain my reasoning using the words mean, average, measure of center, balance point, and data set.
Key Idea / Idea clave
Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data
I Notice / Observo
- How many days of earnings did Miguel record?
- What is the total amount Miguel earned?
I Wonder / Me pregunto
- If Miguel shared the $60 equally across the 4 days, how much would each day be?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Mean Media | The average of a data set. Add all the values, then divide by how many values there are. El promedio de un conjunto de datos. Suma todos los valores y divide entre cuántos valores hay. |
| Average Promedio | Another word for the mean — the amount each value would be if the total were shared equally. Otra palabra para la media: la cantidad que tendría cada valor si el total se repartiera en partes iguales. |
| Measure of center Medida de centro | A single number used to describe the middle, or typical value, of a whole data set. Un solo número que se usa para describir el centro, o valor típico, de todo un conjunto de datos. |
| Balance point Punto de equilibrio | The value where the total distance of the data above it equals the total distance below it. The mean is the balance point. El valor donde la distancia total de los datos por encima es igual a la distancia total por debajo. La media es el punto de equilibrio. |
| Data set Conjunto de datos | The whole collection of values that were gathered or measured. Toda la colección de valores que se recopilaron o midieron. |
| Target mean Media objetivo | The mean a person is trying to reach. La media que una persona intenta alcanzar. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. Find the mean of: 4, 6, 8, 10
- A 6
- B 7
- C 8
- D 28
Answer:
2.
Complete each empty cell. Show your reasoning below.
| Data Set | Total | How Many Values | Mean |
|---|---|---|---|
| 6, 9, 12, 9 | |||
| 20, 14, 16, 18, 22 | |||
| 5, 8, 8, 11, 13, 15 |
3. Sofia wants to average 15 points per game over 10 games. How many points does she need in all 10 games combined?
- A 1.5 points
- B 15 points
- C 25 points
- D 150 points
Answer:
4. Sofia realized she made an error: she actually scored 12 points in Game 8, not 10. Her other games are unchanged (12, 20, 16, 11, 17, 14, 15, and 18). How does this change the number of points she needs in Game 10 to average 15 points per game? Show how you know.
Her new total after 9 games is ___ points. To average 15 over 10 games she still needs ___ points in all, so Game 10 must now be ___ points. That is ___ points fewer than before, because ___.
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: