Numerical Methods for Describing Data From Graphical to

Numerical Methods for Describing Data From Graphical to Numerical

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”: 6 L 5 H 5 L 4 H 4 L 3 H 3 L 0 5 0 0 1 3 3 4 6 6 8 1 1 2 4 4 3 Key: 3 | 3 means 33 Q 1 = 44 Median = 46 IQR = 9 Q 3 = 53 lowest = 33 highest = 60 Five number summary: lowest value, Q 1, median, Q 3, highest value (33, 44, 46, 53, 60) Interquartile range (IQR) = Q 3 – Q 1

Outlier (below): smaller than Q 1 – 1. 5 IQR Outlier (above): larger than Q 3 + 1. 5 IQR 44 – 1. 5(9) = 30. 5 53 + 1. 5(9) = 66. 5 Boxplot 25 33 30 44 35 40 46 53 IQR 1. 5 IQR 45 50 55 Percent of Juice Lost No outliers! 60 60 65

Modified Boxplot Suppose the data set replaces 33 with 28 41 44 28 46 53 60 * 25 30 35 40 1. 5 IQR 45 50 55 Percent of Juice Lost 60 65

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?

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

How the tail pulls the mean MEDIAN = 9 AVERAGES I= 10 III = 9 IV = 9 V= 10 IV VIII V VI = 9 III VI VII IV I II V VI II I 4 6 8 10 12 14 16 MEAN = 9. 33 IX VIII IX VII = 9 VIII = 9 IX = 9 2 18 20

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

How the tail pulls the mean MEDIAN = 9 AVERAGES I= 13 II = 12 III = 11 IV = 11 V= 10 III VI VI = 10 II V VIII VI I IV VII IX MEAN = 10. 44 VIII VII = 9 IX V IV III II I 12 14 16 18 20 VIII = 9 IX = 9 2 4 6 8 10