understandable statistics seventh edition by brase and brase prepared by: lynn smith gloucester...
TRANSCRIPT
![Page 1: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/1.jpg)
Understandable StatisticsSeventh Edition
By Brase and BrasePrepared by: Lynn Smith
Gloucester County College
Chapter Two
Organizing Data
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A graphical display should:
• Show the data
• Induce the viewer to think about the substance of the graphic
• Avoid distorting the message
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Bar Graph• bars of uniform width• uniformly spaced• may be vertical or
horizontal• lengths represent
quantities being compared
• provide title, labels for each bar and lengths of bars
Reasons for Returns
0
10
20
30
40
50
60
Col
or
Size
Did
n't
like
Qua
lity
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Pareto Chart
• tool of quality control• start with a bar chart• arrange bars in
decreasing order of frequency
• frequently used to investigate causes of problems
Reasons for returns
50
20
105
0
10
20
30
40
50
60
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Circle Graph (Pie Chart)
• shows division of whole into component parts
• label parts with appropriate percentages of the whole
Conventions held
49%
27%
19%5%
FloridaCaliforniaVirginiaTexas
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Time Plot
• Shows data values in chronological order
• time on horizontal scale
• variable being measured on vertical scale
• connect data points with line segments
Sales (in thousands of dollars)
050
100150200250300
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Time Series
• Time series are data sets composed of similar measurements taken at regular intervals over time.
• A time plot can reveal some features of a time series.
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Histogram
Differences from a bar chart:
• bars have equal width and always touch
• width of bars represents quantity
• heights of bars represent frequency
f
Measured quantity
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To construct a histogram from raw data:
• Decide on the number of classes (5 to 15 is customary).
• Find a convenient class width.
• Organize the data into a frequency table.
• Find the class midpoints and the class boundaries.
• Sketch the histogram.
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Finding class width
1. Compute:
classesofnumberdesiredvaluedatasmallestvaluedataestargl
2. Increase the value computed to the next highest whole number
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Class Width
Raw Data:
10.2 18.7 22.3 20.0
6.3 17.8 17.1 5.0
2.4 7.9 0.3 2.5
8.5 12.5 21.4 16.5
0.4 5.2 4.1 14.3
19.5 22.5 0.0 24.7
11.4
Use 5 classes.
24.7 – 0.0
5
= 4.94
Round class width up to 5.
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Frequency Table
• Determine class width.
• Create the classes. May use smallest data value as lower limit of first class and add width to get lower limit of next class.
• Tally data into classes.
• Compute midpoints for each class.
• Determine class boundaries.
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Tallying the Data# of miles tally frequency
0.0 - 4.9 |||| | 6
5.0 - 9.9 |||| 5
10.0 - 14.9 |||| 4
15.0 - 19.9 |||| 5
20.0 - 24.9 |||| 5
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Grouped Frequency Table
# of miles f
0.0 - 4.9 6
5.0 - 9.9 5
10.0 - 14.9 4
15.0 - 19.9 5
20.0 - 24.9 5
Class limits:
lower - upper
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Computing Class Width
difference between the lower class limit of one class and the lower class
limit of the next class
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# of miles f class widths
0.0 - 4.9 6 5
5.0 - 9.9 6 5
10.0 - 14.9 4 5
15.0 - 19.9 5 5
20.0 - 24.9 5 5
Finding Class Widths
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Computing Class Midpoints
lower class limit + upper class limit
2
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# of miles f class midpoints
0.0 - 4.9 6 2.45
5.0 - 9.9 5
10.0 - 14.9 4
15.0 - 19.9 5
20.0 - 24.9 5
Finding Class Midpoints
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# of miles f class midpoints
0.0 - 4.9 6 2.45
5.0 - 9.9 5 7.45
10.0 - 14.9 4
15.0 - 19.9 5
20.0 - 24.9 5
Finding Class Midpoints
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# of miles f class midpoints
0.0 - 4.9 6 2.45
5.0 - 9.9 5 7.45
10.0 - 14.9 4 12.45
15.0 - 19.9 5 17.45
20.0 - 24.9 5 22.45
Finding Class Midpoints
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Class Boundaries
(Upper limit of one class + lower limit of next class)
divided by two
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Finding Class Boundaries# of miles f class boundaries
0.0 - 4.9 6
5.0 - 9.9 5 4.95 - 9.95
10.0 - 14.9 4
15.0 - 19.9 5
20.0 - 24.9 5
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Finding Class BoundariesFinding Class Boundaries
# of miles f class boundaries
0.0 - 4.9 6
5.0 - 9.9 5 4.95 - 9.95
10.0 - 14.9 4 9.95 - 14.95
15.0 - 19.9 5
20.0 - 24.9 5
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# of miles f class boundaries
0.0 - 4.9 6
5.0 - 9.9 5 4.95 - 9.95
10.0 - 14.9 4 9.95 - 14.95
15.0 - 19.9 5 14.95 - 19.95
20.0 - 24.9 5
Finding Class Boundaries
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# of miles f class boundaries
0.0 - 4.9 6 ??
5.0 - 9.9 5 4.95 - 9.95
10.0 - 14.9 4 9.95 - 14.95
15.0 - 19.9 5 14.95 - 19.95
20.0 - 24.9 5 19.95 - 24.95
Finding Class Boundaries
![Page 26: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/26.jpg)
# of miles f class boundaries
0.0 - 4.9 6 ?? - 4.95 5.0 - 9.9 5 4.95 - 9.95
10.0 - 14.9 4 9.95 - 14.95
15.0 - 19.9 5 14.95 - 19.95
20.0 - 24.9 5 19.95 - 24.95
Finding Class Boundaries
![Page 27: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/27.jpg)
# of miles f class boundaries
0.0 - 4.9 6 0.05 - 4.95 5.0 - 9.9 5 4.95 - 9.95
10.0 - 14.9 4 9.95 - 14.95
15.0 - 19.9 5 14.95 - 19.95
20.0 - 24.9 5 19.95 - 24.95
Finding Class Boundaries
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# of miles f
0.0 - 4.9 6
5.0 - 9.9 5
10.0 - 14.9 4
15.0 - 19.9 5
20.0 - 24.9 5
Constructing the Histogram
f
| | | | | |
6
5
4
3
2
1
0
-
-
-
-
-
-
--0.05 4.95 9.95 14.95 19.95 24.95 mi.
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Relative Frequency
Relative frequency =
f = class frequency
n total of all frequencies
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Relative Frequency
f = 6 = 0.24
n 25
f = 5 = 0.20
n 25
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# of miles f relative frequency
0.0 - 4.9 6 0.24
5.0 - 9.9 5 0.20
10.0 - 14.9 4 0.16
15.0 - 19.9 5 0.20
20.0 - 24.9 5 0.20
Relative Frequency Histogram
| | | | | |
.24
.20
.16
.12
.08
.04
0
-
-
-
-
-
-
--0.05 4.95 9.95 14.95 19.95 24.95 mi.
Rel
ativ
e fr
eque
ncy
f/n
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Common Shapes of HistogramsCommon Shapes of Histograms
Symmetrical
ff
When folded vertically, both sides are (more or less) the same.
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Common Shapes of HistogramsCommon Shapes of Histograms
Also Symmetrical
ff
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Common Shapes of Histograms
Uniform
ff
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Common Shapes of HistogramsCommon Shapes of Histograms
Non-Symmetrical Histograms
These histograms are skewedskewed..
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Common Shapes of HistogramsCommon Shapes of Histograms
Skewed Histograms
Skewed left Skewed right
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Common Shapes of HistogramsCommon Shapes of Histograms
Bimodal
ff
The two largest rectangles are approximately equal in height and are separated by at least one class.
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Frequency Polygon
A frequency polygon or line graph emphasizes the continuous rise or fall
of the frequencies.
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Constructing the Frequency Polygon
• Dots are placed over the midpoints of each class.
• Dots are joined by line segments.
• Zero frequency classes are included at each end.
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Weights(in pounds) f
2 - 4 6
5 - 7 5
8 - 10 4
11 - 13 5
Constructing the Frequency Polygon
f
| | | | | |
6
5
4
3
2
1
0
-
-
-
-
-
-
- 0 3 6 9 12 15
pounds
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Cumulative Frequency
The sum of the frequencies for that class and all previous or later classes
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Weights (in pounds) f
Greater than 1.5 20
Greater than 4.5 14
Greater than 7.5 9
Greater than 10.5 5
Greater than 13.5 0
Cumulative Frequency Table
Weights(in pounds) f
2 - 4 6
5 - 7 5
8 - 10 4
11 - 13 5
20
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Ogive
Graph of a cumulative frequency table
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Weights (in pounds) f
Greater than 1.5 20
Greater than 4.5 14
Greater than 7.5 9
Greater than 10.5 5
Greater than 13.5 0
Constructing the Ogive
Cu
mu
lati
ve f
req
uen
cy
| | | | | |
20
15
10
5
0
-
-
-
-
- 1.5 4.5 7.5 10.5 13.5 pounds
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Exploratory Data Analysis
• A field of statistical study useful in detecting patterns and extreme data values
• Tools used include histograms and stem-and-leaf displays
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Stem and Leaf Display
Raw Data:
35, 45, 42, 45, 41, 32, 25, 56, 67, 76, 65, 53, 53, 32, 34, 47, 43, 31
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To make a Stem-and-Leaf Display
• Digits of each data value has two parts:
left = “stem,” right = “leaf”
• Align all stems in vertical column in increasing order with a vertical line to their right.
• Place all leaves with same stem on same row as the stem. Rearrange in increasing order
• Label
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Stem and Leaf DisplayFirst data value = 35
Stem and Leaf DisplayFirst data value = 35
2
3
4
5
6
7
stems
5 leaf
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Stem and Leaf DisplaySecond data value = 45
Stem and Leaf DisplaySecond data value = 45
2
3
4
5
6
7
5
5
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Stem and Leaf DisplayThird data value = 42
Stem and Leaf DisplayThird data value = 42
2
3
4
5
6
7
5
5 2
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Stem and Leaf DisplayNext data value = 45
Stem and Leaf DisplayNext data value = 45
2
3
4
5
6
7
5
5 2 5
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Stem and Leaf DisplayNext data value = 41
Stem and Leaf DisplayNext data value = 41
2
3
4
5
6
7
5
5 2 5 1
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Stem and Leaf DisplayNext data value = 32
Stem and Leaf DisplayNext data value = 32
2
3
4
5
6
7
5 2
5 2 5 1
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Stem and Leaf DisplayNext data value = 25
Stem and Leaf DisplayNext data value = 25
2
3
4
5
6
7
5 2
5 2 5 1
5
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Stem and Leaf DisplayNext data value = 56
Stem and Leaf DisplayNext data value = 56
2
3
4
5
6
7
5 2
5 2 5 1
5
6
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Stem and Leaf DisplayNext data value = 67
Stem and Leaf DisplayNext data value = 67
2
3
4
5
6
7
5 2
5 2 5 1
5
6
7
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Stem and Leaf DisplayNext data value = 76
Stem and Leaf DisplayNext data value = 76
2
3
4
5
6
7
5 2
5 2 5 1
5
6
7
6
![Page 58: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/58.jpg)
Stem and Leaf DisplayNext data value = 65
Stem and Leaf DisplayNext data value = 65
2
3
4
5
6
7
5 2
5 2 5 1
5
6
7 5
6
![Page 59: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/59.jpg)
Stem and Leaf DisplayNext data value = 53
Stem and Leaf DisplayNext data value = 53
2
3
4
5
6
7
5 2
5 2 5 1
5
6 3
7 5
6
![Page 60: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/60.jpg)
Stem and Leaf DisplayNext data value = 53
Stem and Leaf DisplayNext data value = 53
2
3
4
5
6
7
5 2
5 2 5 1
5
6 3 3
7 5
6
![Page 61: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/61.jpg)
Stem and Leaf DisplayNext data value = 32
Stem and Leaf DisplayNext data value = 32
2
3
4
5
6
7
5 2 2
5 2 5 1
5
6 3 3
7 5
6
![Page 62: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/62.jpg)
Stem and Leaf DisplayNext data value = 34
Stem and Leaf DisplayNext data value = 34
2
3
4
5
6
7
5 2 2 4
5 2 5 1
5
6 3 3
7 5
6
![Page 63: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/63.jpg)
Stem and Leaf DisplayNext data value = 47
Stem and Leaf DisplayNext data value = 47
2
3
4
5
6
7
5 2 2 4
5 2 5 1 7
5
6 3 3
7 5
6
![Page 64: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/64.jpg)
Stem and Leaf DisplayNext data value = 43
Stem and Leaf DisplayNext data value = 43
2
3
4
5
6
7
5 2 2 4
5 2 5 1 7 3
5
6 3 3
7 5
6
![Page 65: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/65.jpg)
Stem and Leaf DisplayNext data value = 31
Stem and Leaf DisplayNext data value = 31
2
3
4
5
6
7
5 2 2 4 1
5 2 5 1 7 3
5
6 3 3
7 5
6
![Page 66: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/66.jpg)
Stem and Leaf DisplayStem and Leaf Display
2
3
4
5
6
7
5 2 2 4 1
5 2 5 1 7 3
5
6 3 3
7 5
6
![Page 67: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/67.jpg)
Stem and Leaf Display with Leaves Rearranged
Stem and Leaf Display with Leaves Rearranged
2
3
4
5
6
7
1 2 2 4 5
1 2 3 5 5 7
5
3 3 6
5 7
6
![Page 68: Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data](https://reader036.vdocument.in/reader036/viewer/2022062315/5697c0211a28abf838cd2c79/html5/thumbnails/68.jpg)
Stem and Leaf Display with Labeling
Stem and Leaf Display with Labeling
2
3
4
5
6
7
1 2 2 4 5
1 2 3 5 5 7
5
3 3 6
5 7
6
Ages of Employees
2 5 represents 25 years