Measures of Central Tendency MARE 250 Dr. Jason Turner

The measure of central tendency Three most important: Centracidal Tendencies

Mean Girls Mean –

The Median The median is typically defined as

The Mode The mode is typically defined as 30 Number of Individuals

You are so totally skewed! The mean is sensitive to extreme (very large or small) observations and the median is not Mean is Greater than the Median Mean and Median are Equal Mean is Less Than the Median

Resistance Measures A resistance measure is not sensitive to the influences of a few extreme observations Trimmed Means –

How To on Computer On Minitab: Your data must be in a single column Go to the 'Stat' menu, and select 'Basic stats', then 'Display descriptive stats'. Select your data column in the 'variables' box. The output will generally go to the session window, or if you select 'graphical summary' in the 'graphs' options, it will be given in a separate window. This will give you a number of basic descriptive stats, though not the mode.

MARE 250 Dr. Jason Turner Measures of Dispersion and Variability

Measure of Dispersion of the Data – 2 of the most frequently used – Please Disperse!

The Range Range – Range = Max - Min

The Variance Variance -

The Variance Degrees of Freedom - quantity (n -1)

Standard Deviation Standard Deviation –

Quartiles Median divides data into 2 equal parts: 50% bottom, 50% top Quartiles – into quarters – 4 equal parts A dataset has 3 quartiles: Q 1 – Q 2 – Q 3 –

Quartiles

Interquartile Range Interquartile Range (IQR) – IQR = Q 3 – Q 1

Outlier, Outlier Outliers –

Pants on Fire Must deal with outliers: (Yes, really!)

The Outer Limits Lower and Upper Limits: Lower limit – Upper limit –

The Outer Limits If a value is outside the “Outer Limits” of a dataset it is an

Five-Number Summary 5-Number Summary: Min, Q 1, Q 2, Q 3, Max

Boxplot (Box-and-Whisker-Design): Boxplots Q1Q1 Q2Q2 Q3Q3 Min Max 070

Boxplots 070 * Potential Outlier Modified Boxplot – includes outliers

Boxplots

Use the boxplot to assess the symmetry of the data: If the data are fairly symmetric, the median line will be roughly in the middle of the IQR box and the whiskers will be similar in length If the data are skewed, the median may not fall in the middle of the IQR box, and one whisker will likely be noticeably longer than the other Boxplots