Page 361 - Algebra 1

Determining Outliers
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1).
Outliers are any values x such that
x<Q1 -1.5(IQR) or x>Q3 +1.5(IQR)
Example
1
Analyzing a Box-and-Whisker Plot
The box-and-whisker plot shows scores on a history test. Use the interquartile range to identify outliers.
SOLUTION
Test Scores
50 60 70 80 90 100
Math Language
An outlier is a data value that is much greater or much less than the other data values in the set.
first quartile (Q1): 70 third quartile (Q3): 90 interquartile range (IQR): 90 - 70 = 20 → (1.5)20 = 30
70 - 30 = 40 90 + 30 = 120
No values are less than 40 or greater than 120, so there are no outliers.
Displaying Data in a Box-and-Whisker Plot
Make a box-and-whisker plot to display the data of fish lengths (in millimeters) reported by the California Department of Fish and Game.
312, 210, 422, 323, 358, 511, 689, 722, 333, 301, 298, 755, 213, 245, 356
Half of the fish are between which lengths?
SOLUTION
Order the data from least to greatest. Then find the quartiles, median, minimum and maximum values.
Interquartile Range
Math Reasoning
Write In a box-and- whisker plot, what do Q1, Q2, and Q3 represent in a data set?
Example
2
210, 213, 245, 298, 301, 312, 323, 333,
minimum Q1 median Draw a box-and-whisker plot.
Half of the fish are between 298 mm and 511 mm.
356, 358, 422, 511, 689, 722, 755
Q3 maximum Length of Fish
200 300 400 500 600 700 800
In a box-and-whisker plot, outliers are represented by an asterisk (*) and are not included in the whisker.
Displaying Data Including Outliers
The speeds of 10 birds were recorded in miles per hour. 19, 20, 22, 24, 24, 26, 29, 30, 32, 47
Display the data using a box-and-whisker plot. Identify any outliers.
Example
3
346 Saxon Algebra 1