Shape of Data Distributions

6.DS.3 · Unit 8 · Lesson 7

Name   Period

Objectives / Objetivos

Content Objective: I can describe the shape of a data distribution as symmetric, skewed, or having clusters and gaps.

Language Objective: I can explain my description using the words symmetric, skewed, cluster, and gap.

Key Idea / Idea clave

Symmetric data mirrors around the center; skewed data has a long tail, and the skew is named for the direction the tail points.

I Notice / Observo

  • Do the three data sets look the same when graphed?
  • Which graph has data bunched in the middle? Which has a long tail?

I Wonder / Me pregunto

  • Why would different sports data have different shapes?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Symmetric
Simétrico		Data that looks about the same on the left and right.
Datos que se ven casi iguales a la izquierda y a la derecha.
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.
Cluster
Agrupamiento		A group of numbers that are close together.
Un grupo de números que están cerca unos de otros.
Gap
Hueco (espacio)		A big empty space where there is no data.
Un espacio grande y vacío donde no hay datos.
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 histogram of basketball players' ages shows: most players are 22–28, with a long tail of older players up to age 40. What is the shape of this distribution?
    1. Skewed right
    2. Symmetric
    3. Skewed left
    4. Uniform
  2. A dot plot of goals scored per game shows: 0(5 dots), 1(7 dots), 2(4 dots), 3(2 dots), 4(1 dot). What is the shape?
    1. Skewed right — most values at the low end with a tail to the right
    2. Symmetric — equal on both sides
    3. Skewed left — most values at the high end
    4. Uniform — all bars the same height
  3. Match each distribution shape to how its mean and median compare.
  4. Find the Shape Error
    1. Step 1: Data — Sprint times (seconds): 10.2, 10.5, 10.8, 11.0, 11.1, 11.2, 11.3, 11.5, 14.8
    2. Step 2: Histogram — 10.0–10.9: 3, 11.0–11.9: 5, 12.0–12.9: 0, 13.0–13.9: 0, 14.0–14.9: 1
    3. Step 3: Shape — Skewed left because the tall bar is on the right side
    4. Step 4: Best measure — Use the mean because skewed data uses the mean

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

Reflection / Reflexión

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