Describe Distribution: Center, Spread, and Shape

Students describe a distribution of data by its center (where most data cluster), spread (how far apart the data range), and overall shape (symmetric, skewed, uniform). They use these characteristics to compare datasets and draw informal conclusions.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 6 · Statistics and Data Analysis · question 1 of 3

0 of 20

20 rungs. A star at the top.

Describe the spread of windows per house: what range?

Your answer:

How it is taught

0:00 of 5:19

Center is a typical value.

Spread is how wide the data sit.

Read it: Center, spread and shape on a box plot

This box plot's center is its median, the line in the box at 30. Its spread is the IQR, 45 − 20 = 25, and the range, 60 − 5 = 55. Its shape stretches toward the high values: from 30 up to 60 is longer than from 30 down to 5.

Read the line inside the box: the median is the center of the data.
Read the box's edges and the whiskers' ends: the IQR (the box's length) and the range (whisker to whisker) are the spread.
Compare the two sides of the median, down to the least value and up to the greatest: the data stretch out toward the longer side, and equal sides make the plot balanced.

A box plot shows 5 numbers about the data, not every value.

The box holds the middle half of the data.

Each whisker holds the quarter of the data beyond the box, so the plot shows the shape too: here 30 to 60 is longer than 5 to 30, so the data stretch out toward the high values.

The median is the center, the IQR and the range are the spread, and the longer side of the median gives the shape.

Reading the box's length, 25, as the range.

The range runs whisker to whisker: 60 − 5 = 55. The box's length is the IQR.

A box runs from 15 to 25, and its whiskers reach 5 and 40. The IQR is ___ — 10. The IQR is the box's length: 25 − 15 = 10.

Books read by 9 students

Nine students counted how many books they read this month. How can we describe their data?

We made a dot plot. Each dot is one student, stacked above the number of books they read.

First, the center: where do most of the dots cluster?

Right at three! Most students read about three books, so the center is three.

Next, the spread: how far apart is the data, from lowest to highest?

From one book to five books — that's a spread, or range, of four.

Grade 6 · Center, spread, and shape of a dot plot

Finally, the shape: what does the whole pile look like?

It rises to a peak in the middle and falls evenly on both sides. That shape is symmetric.

Center three, spread four, shape symmetric. That's how we describe a distribution!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free