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 (*)
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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
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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
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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
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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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