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STAT 110 - Section 5 Lecture 15
Professor Hao WangUniversity of South Carolina
Spring 2012
Last time: HistogramExample: 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
How would you describe the distribution?
4
5
6
7
8
9
7
5
2
3 6 6 7
4 8 8 9
0 2 3
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, 9leaf – 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
How would you describe the distribution?
4
5
6
7
8
9
7
5
2
3 6 6 7
4 8 8 9
0 2 3
4
5
6
7
8
9
7
5
2
3 6 6 7
4 8 8 9
0 2 3
The smallest observation in this stemplot is
A) 09
B) 39
C) 47
D) 74
E) 93
4
5
6
7
8
9
7
5
2
3 6 6 7
4 8 8 9
0 2 3
This data set is
A) Skewed Left
B) Symmetric
C) Skewed Right
