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Numerical Methods for Describing Data

Numerical Methods for Describing Data. From Graphical to Numerical. 6L 0 5H 5 5L 0 0 1 3 3 4 4H 6 6 6 6 8 4L 1 1 2 4 4 3H 3L 3. Key: 3 | 3 means 33.

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Numerical Methods for Describing Data

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  1. Numerical Methods for Describing Data From Graphical to Numerical

  2. 6L 0 5H5 5L 0 0 1 3 3 4 4H 6 6 6 6 8 4L 1 1 2 4 4 3H 3L 3 Key: 3 | 3 means 33 2. The percentage of juice lost after thawing for 19 different strawberry varieties appeared in the article “Evaluation of Strawberry Cultivars with Different Degrees of Resistance to Red Scale”: Q1 = 44 Median = 46 Q3 = 53 IQR = 9 lowest = 33 highest = 60 Five number summary: lowest value, Q1, median, Q3, highest value (33,44,46,53,60) Interquartile range (IQR) = Q3 – Q1

  3. 33 44 46 53 60 Outlier (below): smaller than Q1 – 1.5IQR Outlier (above): larger than Q3 + 1.5IQR 44 – 1.5(9) = 30.5 No outliers! 53 + 1.5(9) = 66.5 Boxplot IQR 1.5 IQR 25 30 35 40 45 50 55 60 65 Percent of Juice Lost

  4. 41 44 46 53 60 Modified Boxplot Suppose the data set replaces 33 with 28 28 * 1.5 IQR 25 30 35 40 45 50 55 60 65 Percent of Juice Lost

  5. Recap of Numerical Descriptors • Measures of center: mean, median • Measures of variability: spread, range, IQR, variance, standard deviation • Mean, range, spread, variance and standard deviation are nonresistant to outliers. • How does shape affect the measures of center and variability?

  6. How the tail pulls the mean MEDIAN = 9 = MEAN AVERAGES I = 9 II = 9 III = 9 IV = 9 V = 9 VI = 9 VII = 9 VIII = 9 IX = 9 IX IX VIII VIII IV VII VII IV III VI VI III I II V V II I 2 4 6 8 10 12 14 16 18 20

  7. MEAN = 9.33 How the tail pulls the mean MEDIAN = 9 AVERAGES I = 10 II = 10 III = 9 IV = 9 V = 10 VI = 9 VII = 9 VIII = 9 IX = 9 IX VIII IX IV VII VIII V III VI VII IV I II V VI III II I 2 4 6 8 10 12 14 16 18 20

  8. MEAN = 10 How the tail pulls the mean MEDIAN = 9 AVERAGES I = 12 II = 11 III = 10 IV = 10 V = 10 VI = 10 VII = 9 VIII = 9 IX = 9 IX IV VIII III VII IX II VI VIII VI IV I V VII V III II I 2 4 6 8 10 12 14 16 18 20

  9. MEAN = 10.44 How the tail pulls the mean MEDIAN = 9 AVERAGES I = 13 II = 12 III = 11 IV = 11 V = 10 VI = 10 VII = 9 VIII = 9 IX = 9 IX VIII VII III VI IX II V VIII VI I IV VII V IV III II I 2 4 6 8 10 12 14 16 18 20

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