What is Statistics

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• What is Statistics?

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• Statistics is a collection of procedures and
  principles for gathering data and analyzing
  information in order to help people make
  decisions when faced with uncertainty.

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7 Statistical Stories w/Morals

• Speedy Drivers
• Disaster in the Skies
• Dating
• Angry Women
• Prayer Pressure
• Heart Attacks
• Internet Loneliness

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Data are used to make a judgment about a
situation

• What question needs to be answered?
• How should we collect data how much?
• How can we summarize the data?
• What decisions or generalizations can be made in
  regards to the question based on the data
  collected?

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Population Data vs. Sample Data

• Everyoneeverything
• Parameterssummary measurements denoted by greek
  letters (?, ?)

• Representative smaller subset of population
• Statisticssummary measurements denoted by
  standard letters (p, )

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Data--Types of Variables
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Summarizing Dataw/ Bar graph of Categorical Data
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HistogramUnivariate quantitative data
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Comparative BoxplotsUnivariate quantitative data
by category
Outliers
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ScatterplotBivariate quantitative data
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Summary Features of Quantitative Variables
LocationCenter(average) SpreadVariability Shape
Distribution pattern with data
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LocationCenter
Mean(?, ) add up all data values and divide by
number of data values Medianlist data values in
order, locate middle data value
Data Set 19, 20, 20, 21, 22
Mean is
Median is 20 since it is the middle number of the
ranked data values.
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Describing Spread Range, Quartiles, and
Interquartile Range

• Range Maximum minimum
• Q1 (Quartile 1) is the 25th percentile of ordered
  data or median of lower half of ordered data
• Median (Q2) is 50th percentile of ordered data
• Q3 (Quartile 3) is the 75th percentile of ordered
  data or median of upper half of ordered data
• IQR(Interquartile Range) Q3 Q1
• Any point that falls outside the interval
  calculated by Q1- 1.5(IQR) and Q3 1.5(IQR) is
  considered an outlier.

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Boxplot5 Number Summary
Computersx1000 250 1000 2400 3500 5400 8600
1000
2950
5400
8600
250
Q3
Max
min
Q1
median
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Describing Spread Standard Deviation
Roughly speaking, standard deviation is the
average distance values fall from the mean.
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Population and SampleStandard Deviation

• ?2 ?population variance

• s2 ?sample variance

What is Variance?
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Calculated Standard Deviations
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Various Distributions
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Empirical Rule
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34
68
47.5
47.5
95
49.85
49.85
99.7
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Empirical Rule
68
95
99.7
68-95-99.7 RULE
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Empirical Rule-- Let HN(69, 2.52)
What is the likelihood that a randomly selected
adult male would have a height less than 69
inches?
P(h lt 69) .50
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Empirical Rulerestated

• 68 of the values fall within 1 standard
  deviation of the mean in either direction
• 95 of the values fall within 2 standard
  deviation of the mean in either direction
• 99.7 of the values fall within 3 standard
  deviation of the mean in either direction
• Note If the range ? 6 doesnt roughly equal the
  standard deviation, the data may contain outliers
  or have a skewed shape.

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Using the Empirical Rule
Let HN(69, 2.52)
What is the likelihood that a randomly selected
adult male will have a height between 64 and 74
inches?
P(64 lt h lt 74) .95
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Using Empirical Rule-- Let HN(69, 2.52)
What is the likelihood that a randomly selected
adult male would have a height of less than 66.5
inches?
P(h lt 66.5) 1 (.50 .34) .50 - .34
.16
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Using Empirical Rule-- Let HN(69, 2.52)
What is the likelihood that a randomly selected
adult male would have a height of greater than 74
inches?
P(h gt 74) 1 - (.50 .475) 1 -
.975 .025
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Using Empirical Rule-- Let HN(69, 2.52)
What is the probability that a randomly selected
adult male would have a height between 64 and
76.5 inches?
P(64 lt h lt 76.5) .475 .4985
.9735
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Standardized Z-Score

• To get a Z-score, you need to have 3 things
• Observed value of X
• Population mean, ?
• Population standard deviation, ?
• Then follow the formula.

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Empirical Rule Z-Score

• About 68 of values in a normally distributed
  data set have z-scores between 1 and 1 95 of
  the values have z-scores between 2 and 2 and
  99.7 of the values have z-scores between 3 and
  3.

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Z-Score Let HN(69, 2.52)

• What would be the standardized score for an adult
  male who stood 71.5 inches?

HN(69, 2.52) ZN(0, 12)
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Z-Score Let HN(69, 2.52)
What would be the standardized score for an adult
male who stood 65.25 inches?
h 65.25 as z -1.5