displaying & analyzing data
DESCRIPTION
Displaying & Analyzing Data. Stem-and-leaf Plot Box-and-Whisker Plot Venn Diagrams. Statistics: Stem-and-Leaf Plots. Statistics: The branch of mathematics that deals with collecting, organizing, analyzing or interpreting data. Data: Numerical facts or information. - PowerPoint PPT PresentationTRANSCRIPT
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Displaying & Analyzing DataStem-and-leaf PlotBox-and-Whisker PlotVenn Diagrams
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Statistics: The branch of mathematics that deals with collecting, organizing, analyzing or interpreting data.Data: Numerical facts or information.Stem-and-Leaf Plots: A convenient method to display every piece of data by showing the digits of each number.
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In a stem-and-leaf plot, the greatest common place value of the data is used to form stems. The numbers in the next greatest place value position are then used to form the leaves.
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Age of United states Presidents at their First Inauguration: 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 50 47 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 (Through the 40th presidency)
Stem Leaf456
907
9
177 7 1
668
84 42
8
410
745
21 6 15 4 1
5 0
35 6
22
1 9 4
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2 3 6 7 8 9 90 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 80 1 1 1 2 4 4 5 8 9
Stem Leaf
456
Rearrange the leaf in numerical order from least to greatest
Age of United states Presidents at their First Inauguration: 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 50 47 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 (Through the 40th presidency)
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2 3 6 7 8 9 90 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 80 1 1 1 2 4 4 5 8 9
StemLeaf: Age of United States Presidents at their First Inauguration (through the 40th Presidency)
456
It is easy to interpret or analyze information from the Stem-and-Leaf.
1. How many presidents were 51 years old at their inauguration?
2. What age is the youngest president to be inaugurated?
3. What is the age of the oldest president to be inaugurated?
4. How many presidents were 40-49 years old at their inauguration?
442
69
7
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Data Displays
A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set.
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17, 18, 19, 21, 24,26, 27The lower quartile (LQ) is the median of the lower half of the data.The LQ is 18.The upper quartile (UQ) is the median of the upper half of the data. The UQ is 26.
17 18
19 20 21 22 23 24 25 26 282716
___ __
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Make a Box & Whisker Plot
76, 78, 82, 87, 88, 88, 89, 90, 91, 95
88
Find the median of this segment (LQ)
LQ = 82
Find the median of this segment.
UQ = 90
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76, 78, 82, 87, 88, 88, 89, 90, 91, 95
Now for the box and whisker
65 70 75 80 85 90 95
Least
Value
Lower Quartile (LQ)
Middle Quartil
e
Upper Quartil
e
Greatest
Value
100
105
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76, 78, 82, 87, 88, 88, 89, 90, 91, 95
65 70 75 80 85 90 95
Least
Value
Lower Quartile (LQ)
Middle Quartil
e
Upper Quartil
e
Greatest
Value
100
105
What number represents 25% of the data?What number represents 50% of the data?What number represents 75% of the data?
LQ 82
Median 88UQ 90
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Venn Diagrams
Content Standard:
Begin to identify information in a Venn diagram
Click for the next screen.
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The diagram shows the results of your survey on ice cream preferences for 23 friends.
13 81
Click for an answer.
How many of your friends liked chocolate and/or vanilla ice cream?How many students are not in the diagram? Why?
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13 81
The End.
How many students are not in the diagram? Why? 23-22 1
One student is not in the diagram. He must not like chocolate or vanilla ice cream.
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Stem and Leaf PlotStem and leaf plots are used as a quick way of seeing how many pieces of data fall in various ranges. The reader can quickly tell:
- the range - the mode
Stem and leaf plots have a title, a stem, and leavesA key is used to explain how to read the stem and leaves.
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Box - and - Whisker PlotDisplays large set of data.
Gives general idea of how data clusters.
Graph includes: - Title
- Labeled intervals - Box between lower
and upper quartiles - Whiskers from
quartiles to extremes - Median, quartiles
and whiskers labeled
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Displaying & Analyzing DataStem-and-leaf PlotBox-and-Whisker PlotVenn Diagrams