Prentice Hall Algebra 2

Chapter 11 Probability and Statistics > 11-5 Analyzing Data

The range of a set of data is the difference between the greatest and least values. If you order data from least value to greatest value, the median divides the data into two parts. The median of each part divides the data further and you have four parts in all. The values separating the four parts are quartiles. The interquartile range is the difference between the third and first quartiles.

Problem 3 Comparing Data Sets

Temperature The table shows average monthly water temperatures for four locations on the Gulf of Mexico. How can you compare the 12 water temperatures from St. Petersburg with the 12 water temperatures from Key West?

**Gulf of Mexico Eastern Coast Water Temperatures (ºF)**
Location	J	F	M	A	M	J	J	A	S	O	N	D
St. Petersburg, Florida	62	64	68	74	80	84	86	86	84	78	70	64
Key West, Florida	69	70	75	78	82	85	87	87	86	82	76	72
Dauphin Island, Alabama	51	53	60	70	75	82	84	84	80	72	62	56
Grand Isle, Louisiana	61	61	64	70	77	83	85	85	83	77	70	65

SOURCE: National Oceanographic Data Center

Know	Need	Plan
Water temperatures near the two cities	The means, medians, modes, ranges, and interquartile ranges	Order the data. Find the means, medians, modes, minimums, maximums, quartiles, range, and interquartile range.

St. Petersburg:	Key West:
x ¯ = 62 + 64 + 64 + 68 + 70 + 74 + 78 + 80 + 84 + 84 + 86 + 86 12 = 900 12 = 75 ( mean water temperature ) table with 2 rows and 2 columns , row1 column 1 , x bar , column 2 equals . fraction 62 plus 64 plus 64 plus 68 plus 70 plus 74 plus 78 plus 80 plus 84 plus 84 plus 86 plus 86 , over 12 end fraction , row2 column 1 , , column 2 equals , 900 over 12 , equals 75 open . meanwatertemperature . close , end table	x ¯ = 69 + 70 + 72 + 75 + 76 + 78 + 82 + 82 + 85 + 86 + 87 + 87 12 = 949 12 ≈ 79.1 ( mean water temperature ) table with 2 rows and 2 columns , row1 column 1 , x bar , column 2 equals . fraction 69 plus 70 plus 72 plus 75 plus 76 plus 78 plus 82 plus 82 plus 85 plus 86 plus 87 plus 87 , over 12 end fraction , row2 column 1 , , column 2 equals , 949 over 12 , almost equal to , 79.1 , open . meanwatertemperature . close , end table
Modes: 64, 84, and 86	Modes: 82 and 87
Min.: 62; Max.: 86; Range: 86 minus 62 equals 24	Min.: 69; Max.: 87; Range: 87 minus 69 equals 18
Image Long Description	Image Long Description
Interquartile range: Q 3 − Q 1 = 84 − 66 = 18 q sub 3 , minus , q sub 1 , equals 84 minus 66 equals 18	Interquartile range: Q 3 − Q 1 = 85 . 5 − 73.5 = 12 q sub 3 , minus , q sub 1 , equals 85 . 5 minus , 73.5 , equals 12

The range and the interquartile range show the temperatures varying less at Key West than at St. Petersburg. Also, the temperatures at Key West are generally higher.

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Problem 3 Comparing Data Sets

Think

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