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Lecture 3

# STAT 101 Lecture Notes - Lecture 3: Histogram, Unimodality, Minimax

Department
Statistics
Course Code
STAT 101
Professor
haleyjeppson
Lecture
3

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Divides' the' values' into' equal' bins
Histogram
Describing* One*Quantitative* Variable
Picture' of' distribution
Leaf-contains' last' digit'of' values
Stem-contains' the'rest' of'the'values4
None-uniform
One-unimodal
Two-bimodal
Three' or' more-multimodal
Shape-number' of' modes' (peaks)
§Skewed' to'the' right' More' smaller' values' trails' off' to'the'
larger' values' (skewed' means' right' is' smaller)
§Skewed' to'the' left-more' larger' values-trails' off' to' the' smaller'
values' (means' left' is'smaller)
Skewed-more' values' on'one' side
Symmetry
Can' impact' statistical' methods
Outliers' (extreme' values)
Interpreting* Histograms* and* Stem* and* Leaf* Displays
Example:
Modes- 1
Skewed-right
Outliers-4'potential' outliers
(n+1)/2'
Median-middle' value' that' divides' histograms' into' two' parts
Mean-average
Center
Mean' and' median' are' different' when' the' distribution' is'skewed' or' outlier' are'
present
Skewed' to'right-mean' >'median
Skewed' to'left-median' >' mean
Report' range' and' IOR' when' reporting' median
Report' standard' deviation' when' reporting' mean
Range-max-min
We'will' divide' the'data' into'quartiles' ('four' equal' parts)'
(min)------------- (25th percentile)-------------(median)' ------------- (75th
percentile)' --------------(max)
Q1=' median' of' lower' half
Q3=' median' of' upper' half
IRQ=' Q1-Q3
• 5-number' summary-reports' median,' quartiles,' and' max' and' min
5-Number* Summaries
Values' closer' to'mean=' smaller' contribution' to's
Values' further' from' the'mean=' larger' contribution' to's
Standard' deviation-measures' variability' (spread)' from' the' mean
Standard* Deviation
Chapter(Three-Displaying( and(Summarizing( Quantitative(
Data
Saturda y,' Septem ber' 3,' 2016
8:09' AM

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Divides' the' values' into' equal' bins
Histogram
Describing* One*Quantitative* Variable
Picture' of' distribution
Leaf-contains' last' digit'of' values
Stem-contains' the'rest' of'the'values4
Stem-and-Leaf' Display
None-uniform
One-unimodal
Two-bimodal
Three' or' more-multimodal
Shape-number' of' modes' (peaks)
§Skewed' to'the' right' More' smaller' values' trails' off' to'the'
larger' values' (skewed' means' right' is' smaller)
§Skewed' to'the' left-more' larger' values-trails' off' to' the' smaller'
values' (means' left' is'smaller)
Skewed-more' values' on'one' side
Symmetry
Can' impact' statistical' methods
Outliers' (extreme' values)
Interpreting* Histograms* and* Stem* and* Leaf* Displays
Example:
Modes- 1
Skewed-right
Outliers-4'potential' outliers
(n+1)/2'
Median-middle' value' that' divides' histograms' into' two' parts
Add'up'all' the' values' and'divide' by'how'many' points
Mean-average
Center
Mean' and' median' are' different' when' the' distribution' is'skewed' or' outlier' are'
present
Skewed' to'right-mean' >'median
Skewed' to'left-median' >' mean
Report' range' and' IOR' when' reporting' median
Report' standard' deviation' when' reporting' mean
Range-max-min
We'will' divide' the'data' into'quartiles' ('four' equal' parts)'
(min)------------- (25th percentile)-------------(median)' ------------- (75th
percentile)' --------------(max)
Q1=' median' of' lower' half
Q3=' median' of' upper' half
IRQ=' Q1-Q3
• 5-number' summary-reports' median,' quartiles,' and' max' and' min
5-Number* Summaries
Values' closer' to'mean=' smaller' contribution' to's
Values' further' from' the'mean=' larger' contribution' to's
Standard' deviation-measures' variability' (spread)' from' the' mean
Standard* Deviation
Chapter(Three-Displaying( and(Summarizing( Quantitative(
Data
Saturda y,' Septem ber' 3,' 2016 8:09' AM