Cogito
Probability and Statistics · Chapter 1 · Lesson 2
Dot Plots and Histograms
The shape of a distribution.
12 problems · about 21 minutes · TEKS P.S.1.B, S-ID.A.1
What this lesson teaches
The student builds and interprets dot plots and histograms, describing shape and identifying outliers.
- 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.
Warm Up
Straightforward practice. Get the method working first.
5 problemsCounts 9, 4, 2, 1. Skewed which way? 1 right, 2 left.
Answer 1
Why Skewed right.
Why does bin width matter in a histogram?
Answer The same data can appear to have a different shape under different widths.
Why Bin width changes the apparent shape.
Counts 2, 4, 6, 4, 2. Symmetric or skewed? 1 symmetric, 2 skewed.
Answer 1
Why It mirrors about the middle.
Counts 8, 5, 2, 1, 1. Skewed which way? 1 right, 2 left.
Answer 1
Why The tail stretches toward the high values.
Counts 1, 1, 2, 5, 8. Skewed which way? 1 right, 2 left.
Answer 2
Why The tail stretches toward the low values.
Build It Up
The same ideas with more to keep track of.
3 problemsCounts 3, 3, 4, 2. How many values in total?
Answer 12
Why Add them.
A histogram of 100 values uses 2 bins. Is the shape well shown? 1 for yes, 0 for no.
Answer 0
Why Too few bins hides everything.
Counts 5, 1, 0, 1, 5. How many peaks?
Answer 2
Why One at each end.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich are good reasons to investigate an outlier rather than delete it?
Answer It may be the most interesting value in the set; It may reveal a recording error worth fixing
Why Tidiness is not a statistical reason for anything.
Counts 1, 2, 7, 2, 1. Symmetric or skewed? 1 symmetric, 2 skewed.
Answer 1
Why It mirrors about the peak.
The Tail: A distribution has most data on the left and a long tail to the right. Is it skewed right or left? 1 right, 2 left.
Answer 1
Why Skewed right.
The Count: A dot plot shows 6, 5, 3, 1, 0 and 1 marks above the values 1 to 6. How many students in total?
Answer 16
Why 16.