Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can describe the shape of a data distribution as symmetric, skewed, or having clusters and gaps.
Key words
Symmetric — Data that looks about the same on the left and right.
Skewed — When most data sits on one side with a tail on the other.
Cluster — A group of numbers that are close together.
Gap — A big empty space where there is no data.
Data distribution — How the data looks: where it sits and how spread out it is.
Variability — How spread out the numbers are.
Steps
Example 1, bar heights from left to right: 2, 5, 8, 5, 2. The bars rise to a peak in the middle and fall evenly on both sides.
Both sides look like mirror images, so this shape is symmetric.
Example 2, bar heights: 9, 6, 3, 1. The tallest bars are on the left and the bars get shorter going right.
The long tail points to the right, so this shape is skewed right. I name the skew after the tail, not the peak.
Try it
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?
Check your answer
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.
Sentence starter
I know ___ because ___.
Goal: I can explain my description using the words symmetric, skewed, cluster, and gap.