Unit 8 · Standard 6.SP.2
Shape of Data Distributions
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Heights: 60, 62, 64, 66, 68, 66, 64, 62, 60 — rises and falls evenly like a hill
Symmetric
Data that looks about the same on the left and right.
Skewed right: most data low (1,2,2,3,3,3,15) — tail stretches toward the high value
Skewed
Data bunched on one side with a tail on the other.
Scores 18, 19, 20, 21, 22 form a cluster around 20 — they are tightly grouped
Cluster
A group of numbers that are close together.
Data: 5, 6, 7, 8, ___, ___, ___, 20 — the empty space from 9 to 19 is a gap
Gap
A big empty space where there is no data.
Looking at a dot plot or histogram, you can see if data is symmetric, skewed, clustered, or has gaps
Data distribution
How the data looks: where it sits and how spread out it is.
Symmetric data with low variability: tightly packed around the center. Skewed data: spread unevenly
Variability
How spread out the numbers are.
Key Ideas & Notes
- The league analyst is studying three different data sets from the season: (1) Player heights across all teams, (2) Number of 3-pointers per game by each player, and (3) Years of experience for all coaches.
- Each data set has a different shape when graphed.
- Your job is to describe each shape and explain what it tells us about the data.
Think About It
- Do the three data sets look the same when graphed?
- Which graph has data bunched in the middle? Which has a long tail?
- Are there any gaps or clusters you can spot?
My Notes
Guided Examples
Example 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?
Solution: Most data is on the left (younger ages) with a tail stretching right (older ages). This is skewed right.
Answer: A. Skewed right
Example 2
A data set is symmetric. What is likely true about the mean and median?
Solution: In a symmetric distribution, the mean and median are approximately equal because the data is balanced on both sides.
Answer: A. They are approximately equal
Example 3
Which word describes the direction of the TAIL, not the peak?
Solution: The skew direction is named after the TAIL. If the tail stretches to the right, it is skewed right, even though the peak is on the left.
Answer: A. Skew — the direction of the long tail tells you the skew direction
Write About the Math The Writing Revolution
I can explain my description using the words symmetric, skewed, cluster, and gap.
1. Kernel Sentence subject + verb
Model: Data distribution is how the data looks: where it sits and how spread out it is.Distribución de datos es cómo se ven los datos: dónde están y qué tan separados están.
Write a kernel sentence about data distribution. Use a subject and a verb.Escribe una oración base sobre distribución de datos. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Data distribution matters in mathDistribución de datos importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Data distribution matters in math because ___.Distribución de datos importa en matemáticas porque ___.
Data distribution matters in math, but ___.Distribución de datos importa en matemáticas, pero ___.
Data distribution matters in math, so ___.Distribución de datos importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about data distribution.Di un hecho verdadero sobre data distribution.
Data distribution ___.
Ask a question about data distribution.Haz una pregunta sobre data distribution.
How does ___ ?¿Cómo ___ ?
Show excitement about data distribution.Muestra entusiasmo sobre data distribution.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with data distribution.Dile a un compañero qué hacer con data distribution.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The data is ___ shaped.Los datos tienen forma de ___.
Most of the data is ___.La mayoría de los datos está ___.
The shape tells me ___.La forma me dice ___.
Try It
Solve on your own. Check the answer key when you are done.
1. 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?
- Skewed right — most values at the low end with a tail to the right
- Symmetric — equal on both sides
- Skewed left — most values at the high end
- Uniform — all bars the same height
2. Match the data shape with the best measure of center.
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A teacher shows two dot plots of quiz scores from two different classes. Class A's data is symmetric with a cluster around 80. Class B's data is skewed right with most scores between 60–70 and a few scores near 100. Compare the classes: which has a higher median? Which has a higher mean? In which class does the mean better represent a typical score?
Sentence starter: Class A is ___ with scores clustered around ___. Class B is skewed ___ with most scores at ___. Class A likely has a ___ median. Class B's mean is pulled ___ by the high scores. The mean better represents a typical score in Class ___ because ___.
Reflect — Exit Ticket
A data set has most values clustered between 40–60, with a few values at 90–100. What is the shape of the distribution and which measure of center is best?
- Skewed right; use median
- Symmetric; use mean
- Skewed left; use median
- Uniform; use mean
Answer Key & Teacher Guide
- Try It 1: A. Skewed right — most values at the low end with a tail to the right — The data peaks at 0–1 goals and tails off toward 4. Most data is on the left with fewer values stretching right — this is skewed right.
- Try It 2:
- Exit Ticket: A. Skewed right; use median — The data clusters on the left (40–60) with a tail to the right (90–100). This is skewed right. The median is best because the mean would be pulled toward the high values.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Data distribution is how the data looks: where it sits and how spread out it is.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).