Download Lecture 8 10192016

MAT 135
Introductory Statistics and Data Analysis
Adjunct Instructor
Kenneth R. Martin
Lecture 8
October 19, 2016
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Agenda
• Housekeeping
– Readings
– HW #5
– Quiz #2
• Chapter 1, 14, 10, 2, & 3
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Housekeeping
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Read, Chapter 1.1 – 1.4
Read, Chapter 14.1 – 14.2
Read, Chapter 10.1
Read, Chapter 2
Read, Chapter 3
Read, Chapter 4
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Housekeeping
• HW #5 issued
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Housekeeping
• Quiz #2
– Wednesday, October 26th
– Chapter 3 material
– Same format as Quiz #1
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Review
• What have we learned so far ?
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Statistics
Standard Deviation - Example
B = {50, 150, 300, 450, 550}
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Statistics
Normal Curve
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AKA, Gaussian distribution
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Mean, Median, and Mode have the approx. same value.
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Associated with mean () at center and dispersion ()
X  N(,) [when a random variable x is distributed normally]
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Observations have equal likelihood on both sides of mean
*** When data is normally distributed, Mean is used to describe
Central Tendency
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The graph of the associated distribution is called “Bell
Shaped”
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Statistics
Standard Normal Curve - Distribution of Data
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Statistics
Standard Normal Curve - Distribution of Data
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Statistics
Measures of Dispersion – Chebyshev’s Theorem
•
Specifies the minimum proportions of the spread of
data in terms of SD
•
Applies to any distribution, regardless of shape.
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Statistics
Measures of Dispersion – Chebyshev’s Theorem
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Statistics
Measures of Dispersion – Chebyshev’s Theorem
μ
σ
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Statistics
Chebyshev’s Theorem - Example
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Statistics
Chebyshev’s Theorem - Example
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Statistics
Chebyshev’s Theorem - Example
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Statistics
Measures of Position – Percentiles
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Percentiles are divisions of data in 100 equal
groups.
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Percentiles are measures to indicate the position of
an individual data point within a group.
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Thus, a percentile ranking of a data point indicates its
position in the data set, with respect to the other data
points.
Percentile graphs are the same as Cum. Freq.
graphs using percentages.
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Statistics
Measures of Position – Percentiles
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Statistics
Measures of Position – Percentiles
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Statistics
Percentiles - Example
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Statistics
Percentiles - Example
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Statistics
Percentiles - Example
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Statistics
Percentiles - Example
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Statistics
Percentiles - Example
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Statistics
Box and Whisker Plot – Boxplot
 Simple graphical tool to summarize data.
 Need to determine 5 values (five-number summary)
from data, to generate a boxplot:
1.
2.
3.
4.
5.
Median (2nd Quartile)
Maximum data value
Minimum data value
1st Quartile (value above 1/4 observations) [whisker]
3rd Quartile (value above 3/4 observations) [whisker]
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Statistics
Box and Whisker Plot – Boxplot Example
• Process aim = 9.0 minutes
• Spec = + / - 1.5 minutes
• n = 125
• R = 1.7
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Statistics
Box and Whisker Plot - Boxplot Example
 Inside box is the median value, and approximately
50% of observations
 Whiskers extend from the box to extreme values
•
Example:
1.
2.
3.
4.
5.
Median; n=125: Median = 63rd value = 9.8
Max = 10.7
Min = 9.0
1st Quartile = X 125 * 0.25 ~ X Avg 31 & 32 value = 9.6
3rd Quartile = X 125 * 0.75 ~ X Avg 94 & 95 value = 10.0
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Statistics
Box and Whisker Plot - Boxplot Example
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Long Whiskers denote the existence of values much
larger than other values.
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For this example, mean  median.
Variants exist, i.e. + / - 1.5*IQR [whisker ends], all
other points are “outliers” as depicted as asterisks
•
IQR = Inner Quartile Range
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Statistics
Box and Whisker Plot - Boxplot Example
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Statistics
Measures of Variability (Dispersion) - IQR
• IQR – Interquartile Range
IQR = Q3 – Q1
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Statistics
Box and Whisker Plot - Boxplot Example
•
For this example,
IQR = ?
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