A dot plot puts one mark above each value; nothing is lost. A histogram groups values into intervals and draws a bar for each count, handling large sets. Skew is named for the direction of the tail. An outlier sits far from the rest.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Building a dot plot
Data 2, 3, 3, 4, 4, 4, 5, 5, 9: one dot at 2, two at 3, three at 4, two at 5, one at 9. The pile peaks at 4 and the 9 stands alone on the right.
Bin width matters
Too few bins hides the shape; too many leaves a jagged mess. Fifty test scores in bins of 10 show a clean hump; in bins of 1 they show noise. Try two widths before trusting a histogram.
Shapes
Symmetric: heights. Skewed right, a long tail of high values: incomes, house prices. Skewed left: exam scores on an easy test, piled near 100 with a tail down. Two peaks: heights of a mixed group of adults and children.
Skew names the tail
Skewed right means the tail stretches right, even though most of the data sits on the left. Ask which way the tail points, not where the pile is.
Outliers
A 9 among 2 to 5 may be a typing error, or the one student with a large family. Investigate before deciding. Removing a real value because it is inconvenient is not analysis.
The one-sentence description
"The distribution of pets is skewed right, centered near 2, spread from 1 to 6, with a possible outlier at 6." Shape, center, spread, outlier, in that order, every time.
Step 2: Try It Yourself
Tap and try it out.
Data: 2, 3, 3, 4, 4, 4, 5, 5, 9. Build the dot plot in words and describe the distribution
- 12: one dot; 3: two; 4: three; 5: two; 9: oneone mark per value
Step 0 of 4
123456
Number of pets16 things were measured in all.
The tallest column is at 1, with 6 marks.
Step 3: In Real Life
Commute times
Twenty commute times as dots show every person. Two hundred, in ten-minute bins, are a histogram. The shape, skewed right by a few long drives, is what a city planner reads first.
Step 4: Watch an Example
One step at a time.
Watch Marcus Describe a Distribution
Marcus has a dot plot of pets owned, piled at 1 and 2 with one student at 6.
- Step 1
Most of the data sits at the low end, with a long thin tail reaching right, so the distribution is skewed right.
Step 5: Your Turn
Practice makes it stick.
The Tail
Problem 1 of 2
A distribution has most data on the left and a long tail to the right. Is it skewed right or left?
The Count
Problem 2 of 2
A dot plot shows 6, 5, 3, 1, 0 and 1 marks above the values 1 to 6. How many students in total?
Read the Shape
1 of 8
Counts 2, 4, 6, 4, 2. Symmetric or skewed?
2 of 8
Counts 8, 5, 2, 1, 1. Skewed which way?
3 of 8
Counts 1, 1, 2, 5, 8. Skewed which way?
4 of 8
Counts 3, 3, 4, 2. How many values in total?
5 of 8
A histogram of 100 values uses 2 bins. Is the shape well shown?
6 of 8
Counts 5, 1, 0, 1, 5. How many peaks?
7 of 8
Which are good reasons to investigate an outlier rather than delete it?
8 of 8
Counts 1, 2, 7, 2, 1. Symmetric or skewed?
Step 6: Quick Check
Show what you know.
Question 1 of 2
Counts 9, 4, 2, 1. Skewed which way?
Question 2 of 2
Why does bin width matter in a histogram?
What You Learned
- A dot plot keeps every value; a histogram groups them into bins.
- Skew is named for the direction of the tail, not the pile.
- Investigate an outlier before deciding what to do with it.
- Describe shape, center, spread and outliers, in one sentence.