04 Describing Data Graphically and Numerically Part 3

# Outliers lower 1st median 3rd upper limit quartile

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Outliers Lower 1st Median 3rd Upper Limit Quartile Quartile Limit * * The lower limit is Q 1 – 1.5 (Q 3 Q 1 ) The upper limit is Q 3 + 1.5 (Q 3 – Q 1 )

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Box and Whisker Plot 18 Constructing a Box and Whisker Plot: Sort values from lowest to highest Find Q 1 , Q 2 , Q 3 Draw the box so that the ends are at Q 1 and Q 3 Draw a vertical line through the median Calculate the interquartile range (Q 3 – Q 1 ) Extend dashed lines from each end to the highest and lowest values within the limits Identify outliers with an asterisk (*)
Box and Whisker Plot Example 19 From our previous example, Q 1 =3465 and Q 3 =3600. This box contains the middle 50% of the data. A vertical line is drawn in the box at the location of the median 300 0 400 0 320 0 340 0 360 0 3800 Q 1 Q 3 Media n

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Box and Whisker Plot Example 20 From our previous example, Q 1 =3465 and Q 3 =3600. This box contains the middle 50% of the data. A vertical line is drawn in the box at the location of the median The limits for the box plot are 1.5(IQR) below Q 1 and 1.5(IQR) above Q 3 . IQR=Q 3 -Q 1 =3600-3465=135. Thus, the limits are 3465-1.5(135)=3262.5 and 3600+1.5(135)=3802.5. Data outside these limits are considered outliers. 300 0 IQR 400 0 320 0 340 0 360 0 3800 1.5(IQ R) 1.5(IQ R) Lower Limit Upper Limit Q 1 Q 3 Media n
Box and Whisker Plot Example 21 From our previous example, Q 1 =3465 and Q 3 =3600. This box contains the middle 50% of the data. A vertical line is drawn in the box at the location of the median The limits for the box plot are 1.5(IQR) below Q 1 and 1.5(IQR) above Q 3 . IQR=Q 3 -Q 1 =3600-3465=135. Thus, the limits are 3465-1.5(135)=3262.5 and 3600+1.5(135)=3802.5. Data outside these limits are considered outliers. The whiskers are drawn from the ends of the box to the limits. 300 0 IQR 400 0 320 0 340 0 360 0 3800 1.5(IQ R) 1.5(IQ R) Lower Limit Upper Limit Q 1 Q 3 Media n

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Box and Whisker Plot Example 22 From our previous example, Q 1 =3465 and Q 3 =3600. This box contains the middle 50% of the data. A vertical line is drawn in the box at the location of the median The limits for the box plot are 1.5(IQR) below Q 1 and 1.5(IQR) above Q 3 . IQR=Q 3 -Q 1 =3600-3465=135. Thus, the limits are 3465-1.5(135)=3262.5 and 3600+1.5(135)=3802.5. Data outside these limits are considered outliers. The whiskers are drawn from the ends of the box to the limits. The location of each outlier is shown with the symbol * * 300 0 IQR 400 0 320 0 340 0 360 0 3800 1.5(IQ R) 1.5(IQ R) Lower Limit Upper Limit Outlier Q 1 Q 3 Media n
Distribution Shape and Box and Whisker Plot Right-Skewed Left-Skewed Symmetric Q 1 Q 2 Q 3 Q 1 Q 2 Q 3 Q 1 Q 2 Q 3

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Descriptive Procedures Center and Location Mean Median Mode Other Measures of Location Weighted Mean Describing Data Numerically Variation Varianc e Standard Deviation Coefficient of Variation Range Percentiles Interquartile Range Quartiles
Measures of Variability 25 It is often desirable to consider measures of variability Measures of variation give information on the spread or variability of the data values.

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