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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

•Spread-how' spread' out'are' the' data' points?

•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

•Interquartile' range-measures' variation' (spread)

Spread

• 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

•Spread-how' spread' out'are' the' data' points?

•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

•Interquartile' range-measures' variation' (spread)

Spread

• 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

###### You're Reading a Preview

Unlock to view full version