STAT 110 - Section 5
Lecture 15
Professor Hao Wang
University of South Carolina
Spring 2012
Last time: Histogram
Example: Mid-term grades
When describing a data set, the three keys are:
1. Shape
2. Center
3. Spread
The histogram is one of the tools to help us with the
shape.
symmetric – the right and left sides of the
histogram are approximately mirror
images of each other
Symmetric example: Human IQ
Symmetric example: Human Height
skewed left – the left side of the histogram
(the half containing the smaller values)
extends much farther than the right
skewed left example: our mid-term
grades
skewed left example: stock returns
skewed right – the right side of the histogram
(the half with the larger values)
extends much farther than the left
skewed right example: income
skewed right example: BMI
unimodal – the histogram has one major spike or
tall area, and the values tend to get smaller
on either side of it; bimodal would be two
major spikes or tall areas
Bimodal example: old faith geyser
duration of eruption
The graph to the right is:
A) Skewed Right
B) Skewed Left
C) Symmetric
D) Bimodal
E) Two of the Above
The graph to the right is:
A) Skewed Right
B) Skewed Left
C) Symmetric
D) Bimodal
E) Two of the Above
The graph to the right is:
A) Skewed Right
B) Skewed Left
C) Symmetric
D) Bimodal
E) Two of the Above
Stemplots
Test score data: 88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88,
47, 77, 93
Stemplot of Test Score Data
4
7
5
5
6
2
7
3667
8
4889
9
023
How would you describe
the distribution?
Stemplots
• When you have small data sets, stemplots are a
good way to display the data.
Advantages over Histograms:
1. quicker to make
2. presents more detailed information
Stemplots
To make a stemplot:
1. Separate each observation into a stem
and a leaf.
2. Write the stems in a vertical column with
the smallest at the top.
3. Draw a vertical line at the right of this
column.
4. Write each leaf in the row to the right of its
stem, in increasing order out from the
stem.
Stemplots
• So, what’s a stem and what’s a leaf?
• A stem consists of all but the final (rightmost)
digit.
• A leaf is the final digit.
• Stems may have as many digits as needed.
• Each leaf contains only a single digit.
Stemplots
Back to our test score data set…
88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93
1. Separate into stem and leaf.
stem – 8, 9, 6, 7, 8, 8, 9, 7, 5, 7, 8, 4, 7, 9
leaf – 8, 0, 2, 6, 4, 9, 2, 3, 5, 6, 8, 7, 7, 3
2. Write stems in vertical column – 4, 5, 6, 7, 8, 9
3. Draw the vertical line.
4. Write each leaf.
Stemplots
Stemplot of Test Score Data
4
7
5
5
6
2
7
3667
8
4889
9
023
How would you describe
the distribution?
4
7
5
5
6
2
7
3667
8
4889
9
023
The smallest observation in
this stemplot is
A) 09
B) 39
C) 47
D) 74
E) 93
4
7
5
5
6
2
7
3667
8
4889
9
023
This data set is
A) Skewed Left
B) Symmetric
C) Skewed Right