1. Numerical Methods for Describing Data
From Graphical to Numerical

2. Interquartile range (IQR) = Q3 – Q1
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”:
6L 0
5H 5 5L 4H 4L 3H
3L 3
Key: 3 | 3 means 33
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. Outlier (below): smaller than Q1 – 1.5IQR
Outlier (above): larger than Q IQR
44 – 1.5(9) = 30.5
No outliers!
(9) = 66.5
Boxplot 33 44 46 53 60
1.5 IQR
IQR
Percent of Juice Lost

4. Modified Boxplot Suppose the data set replaces 33 with 28 *41 28 44 46 53 60 *
1.5 IQR
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

7. 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
MEAN = 9.33 IX
VIII IX IV
VII
VIII V
III VI
VII IV I II V VI
III II I

8. 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
MEAN = 10 IX IV
VIII
III
VII IX II VI
VIII VI IV I V
VII V
III II I

9. 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
MEAN = 10.44
VIII
VII
III VI IX II V
VIII VI I IV
VII V IV
III II I