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# Center 5#Summary

## on Sep 11, 2008

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## Center 5#SummaryPresentation Transcript

• Numerically
• Mean: arithmetic average, add all observations together and divide by the number of observations.
• If there are n observations which are labeled as ;
• The mean is
• Must be written with the bar!!!!
•
• the middle obsevation
• Arrange the data in order from least to greatest
• If an odd number of obs. find the middle number
• If an even number of obs. find the average of the middle two numbers
• Order:
• 2 2 3 4 5 5 6 6 7 7 7 7 7 8 9 9 9 10 11 12 14 16 19 27 35
• Med =
• If the distribution is symmetric the mean the median will be approximately the same
• If the distribution is skewed to the left, the mean will be less than the median
• If the distribution is skewed to the right, the mean will be higher than the median
• The mean is affected by outliers and the median is resistant to outliers
• When the data is symmetric use the mean
• When the data is skewed use the median
• Numeric description of the distribution
• Minimum
• 1 st Quartile (Q 1 ) – Middle number of the bottom half of the data
• Median
• 3 rd Quartile (Q 3 ) – Middle number of the top half of the data
• Maximum
• Put data in order
• 2 2 3 4 5 5 6 6 7 7 7 7 7 8 9 9 9 10 11 12 14 16 19 27 35
Min = 2 Q 1 = 5.5 Med = 7 Q 3 = 11.5 Max = 35
• Graphical display of 5 number summary
• Range = Max – Min
•
• Interquartile Range
• IQR = Q 3 – Q 1
• Any observation below the Lower Fence (LF) or above the Upper Fence (UF) is considered an outlier
• LF = Q 1 – 1.5(IQR)
• UF = Q 3 + 1.5(IQR)
• If outliers are present the whisker extends to the last value not an outlier
• The outlier is marked with an x, box, or point