The Five-Number Summary
Lecture 16
Sections 5.3.1 - 5.3.3
Robb T. Koether
Hampden-Sydney College
Tue, Sep 20, 2011
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Five Number Summary - Robb T. Koether, Summaries of Statistics
Five number theory in describes homework review, percentiles and quartiles, TI-83 five number summary and interquartile ranges.
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The Five-Number Summary
Lecture 16 Sections 5.3.1 - 5.3.
Robb T. Koether
Hampden-Sydney College
Tue, Sep 20, 2011
Outline
(^1) Homework Review
(^2) Percentiles and Quartiles
(^3) The Five-Number Summary
(^4) TI-83 Five-Number Summary
(^5) The Interquartile Range
(^6) Percentiles in Excel
(^7) Assignment
Exercise 5.3, p. 311.
A professor teaches two statistics classes. The morning class has 25 students, and their average on the first test was 82. The evening class has 15 students, and their average on the same test was 74. What is the average on this test if the professor combines the scores for both classes?
Exercise 5.3, p. 311.
A professor teaches two statistics classes. The morning class has 25 students, and their average on the first test was 82. The evening class has 15 students, and their average on the same test was 74. What is the average on this test if the professor combines the scores for both classes?
This would be a weighted average.
Outline
(^1) Homework Review
(^2) Percentiles and Quartiles
(^3) The Five-Number Summary
(^4) TI-83 Five-Number Summary
(^5) The Interquartile Range
(^6) Percentiles in Excel
(^7) Assignment
Percentiles and Quartiles
Definition (pth^ Percentile)
The pth^ percentile of a set of numbers is a number that divides the lower p% of the numbers from the rest.
Definition (1st Quartile)
The 1st quartile, denoted Q 1 , of a set of numbers is the 25th^ percentile.
Definition (3rd Quartile)
The 3rd quartile, denoted Q 3 , of a set of numbers is the 75th^ percentile.
Example
Example (Quartiles)
Find the median and quartiles of the following sample.
Example
Example (Quartiles)
Find the median and quartiles of the following sample.
Median
Example
Example (Quartiles)
Find the median and quartiles of the following sample.
Q 1 Median Q 3
Outline
(^1) Homework Review
(^2) Percentiles and Quartiles
(^3) The Five-Number Summary
(^4) TI-83 Five-Number Summary
(^5) The Interquartile Range
(^6) Percentiles in Excel
(^7) Assignment
Example
Example (Five-Number Summary)
The five-number summary of the previous sample is Min= 5. Q 1 = 10. Med= 19. Q 3 = 25. Max= 32.
5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32
Min Q 1 Median Q 3 Max
Practice
Practice
Find the five-number summary of the Plant B data from Exercise 4.36, page 262. 27 29 31 32 32 33 33 34 37 44 46 51 56 56 57 58 58 59 62 63
TI-83 Five-Number Summary
TI-83 Five-Number Summary
Follow the same procedure that was used to find the mean. When the list of statistics appears, scroll down to the ones labeled minX, Q1, Med, Q3, maxX. They are the five-number summary.
TI-83 Five-Number Summary
TI-83 Five-Number Summary
Use the TI-83 to find the five-number summary of the rainfall data 5.94 1.11 9.52 0.08 6.14 8. 2.93 2.03 3.60 14.71 4.01 0. 6.89 11.07 4.42 3.41 2.85 2. 1.92 5.15 1.58 4.44 0.77 4. 1.15 3.02 1.73 2.60 2.56 10.