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Understanding Skewness and Outliers in Data: Mean vs Median, Summaries of Mathematical Statistics

University of Central Oklahoma (UCO)Mathematical Statistics

The concept of skewness in data distribution and the importance of using the mean or median as a measure of central tendency depending on the presence of outliers. It also discusses the role of standard deviation and interquartile range in measuring spread. Examples of symmetric, skewed left, and skewed right distributions, and provides guidelines for choosing between mean and median based on the shape and presence of outliers.

Typology: Summaries

2021/2022

Uploaded on 09/27/2022

parvini 🇺🇸

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SKEWED TO THE RIGHT

-Here the mean is

pulled right by the

large values.

-The mean is larger

than the median and

not a good measure

of center.

SYMMETRIC

-Mean and the

Median should be

approximately the

same value

SKEWED LEFT

-Mean is pulled

lower by the

smaller values in

the plot

-The mean is

smaller than the

median and is not

a good measure of

center.

Partial preview of the text

Download Understanding Skewness and Outliers in Data: Mean vs Median and more Summaries Mathematical Statistics in PDF only on Docsity!

SKEWED TO THE RIGHT-^ Here the mean ispulled right by thelarge values.-^ The mean is largerthan the median andnot a good measureof center.

SYMMETRIC-^ Mean and theMedian should beapproximately thesame value

SKEWED LEFT-^ Mean is pulledlower by thesmaller values inthe plot-^ The mean issmaller than themedian and is nota good measure ofcenter.

UPPER OUTLIERS-^ Pulls Mean higher-^ Pulls St. Dev.higher-^ Pulls Max higher-^ Pulls Range higher LOWER OUTLIERS-^ Pulls Mean lower-^ Pulls St. Dev.higher-^ Pulls Min lower-^ Pulls Range higherMedianQ1Q3IQR

Unaffected by outliersResistant

Shape •^ Same as before •^ Skewed Left; Skewed Right; Symmetric; Uniform •^ Unimodal; Bimodal; Multimodal; Uniform •^ Outliers?

`^ Mean or Median`^ If Symmetric, Unimodal, with no big Outliers– Use the Mean `^ If Skewed or has big Outliers– Use the Median

Skewed LeftUnimodalOutliers below LF of 63.5Centered at the Median of 91Spread with an IQR of 13Range from 55 to
Skewed RightUnimodalNo OutliersCentered at the Median of 41Spread with an IQR of 70Range from 10 to