Describe a Distribution · MCAP 6.SP.A.2

Learning Goal: Describe a set of data by its center, its spread, and its overall shape.

Vocabulary

distributionThe way data values are spread out or grouped across all the possible values.

centerA single value that is 'typical' for the data, such as the mean or median.

spreadHow far apart the data values are; also called variability.

shapeThe overall pattern of the data, such as symmetric, skewed, or having clusters or peaks.

outlierA value that is much higher or much lower than most of the data.

What You Need to Know

To describe a distribution, always talk about CENTER, SPREAD, and SHAPE.
Center = what is typical (mean or median).
Spread = how much the values vary (range, IQR, or MAD).
Shape words: symmetric (balanced both sides), skewed (a tail pulls one way), peaks, gaps, and clusters.
An outlier is far from the rest of the data and can pull the mean toward it.
Skewed right = tail goes toward larger values; skewed left = tail goes toward smaller values.

Worked Example I Do — watch how it works

A dot plot of pets per student shows: 0,1,1,2,2,2,3,3,4,5. Describe its center, spread, and shape.

Step 1. Center: the data piles up most at 2 (the peak), and the median is 2, so a typical value is about 2 pets.
Step 2. Spread: values run from 0 to 5, so the range is 5 − 0 = 5.
Step 3. Shape: most values are small with a tail stretching to 5, so it is skewed right.

Answer: Center ≈ 2 pets, range = 5, shape is skewed right.

Guided Practice We Do — try it together

1. Data: 1,2,2,2,3 — what is the shape near the center?
💡 Hint: Where does the data pile up?
2. Data: 1,1,1,2,9 — name the value that is an outlier.
💡 Hint: Which value is far from the rest?
3. Data: 2,3,3,4,4,4,9 — is it skewed left or right?
💡 Hint: Which side has the long tail toward the extreme value?

Independent Practice You Do — show your work

1. Data: 5,6,6,6,7,7,8. Is the shape roughly symmetric or skewed?
2. Data: 10,11,11,12,20. Identify the outlier.
3. Data: 1,5,5,5,5,6. Where is the peak (most common value)?
4. Data: 2,2,3,3,4,15. Skewed left or skewed right?
5. Data: 3,4,4,5,5,5,6,6,7. Give the range as a measure of spread.

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.SP.A.2.

Item 1Selected Response6.SP.A.2

A distribution has a long tail stretching toward the high values. How is it described?

Select the correct answer.

○ A. Symmetric○ B. Skewed left○ C. Skewed right○ D. Has no shape

Item 2Selected Response6.SP.A.2

Which three things should you describe about a distribution?

Select the correct answer.

○ A. Color, size, weight○ B. Center, spread, shape○ C. Mean only○ D. Mode and color

Item 3Constructed Response6.SP.A.2

Data set: 4,4,5,5,5,6,18. Name the outlier and tell how it affects the shape.

Enter your answer in the space provided. Show your work.

Enter your answer:

Teacher Answer Key (click to show)

Independent 1	Roughly symmetric — balanced around the peak at 6.
Independent 2	20 is the outlier.
Independent 3	The peak is at 5.
Independent 4	Skewed right (tail toward 15).
Independent 5	Range = 7 − 3 = 4.
Item 1 · 6.SP.A.2	C — When the tail points toward larger values, the distribution is skewed right.
Item 2 · 6.SP.A.2	B — A distribution is described by its center, spread, and overall shape.
Item 3 · 6.SP.A.2	18 is the outlier; it makes the distribution skewed right. — 18 is far above the rest, creating a tail toward the high end (skewed right).

Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.SP.A.2