Lecture 16 Sections Tue, Sep 23, 2008
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1 s Lecture 16 Sections Hampden-Sydney College Tue, Sep 23, 2008 in
2 Outline s in s in 7
3 s Exercise 5.7, p (a) average (or mean) age for 10 adults in a room is 35 years. A 32-year-old adult new enters the room. Can you find the new average age for the 11 adults? If so, find it. If not, explain why not. (b) median age for 10 adults in a room is 35 years. A 32-year-old adult new enters the room. Can you find the new median age for the 11 adults? If so, find it. If not, explain why not. in
4 s Solution (a) If the average age of 10 adults is 35, then the total of their ages must be year-old makes the total 382, so the new average is = in
5 s Solution (b) In this case, we cannot find the new median. We know that half the people in the room are 35 or less, but we do not know how their ages are distributed. For example, if they are all 30, then the 32-year-old would be the new median. On the other hand, if they were all 34, then the new median would be 34. in
6 s in Definition (p th percentile) p th percentile of a set of numbers is a number that divides the lower p% of the numbers from the rest. Definition (1st quartile) 1st quartile, denoted Q 1, of a set of numbers is the 25 th percentile. Definition (3rd quartile) 3rd quartile, denoted Q 3, of a set of numbers is the 75 th percentile.
7 Finding Quartiles s To find the quartiles, first find the position of the median. n the 1st quartile is the median of all the numbers that are below that position. 3rd quartile is the median of all the numbers that are above that position. in
8 s (Quartiles) Find the median and quartiles of the following sample. 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32 in
9 s (Quartiles) Find the median and quartiles of the following sample. 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32 Median in
10 s (Quartiles) Find the median and quartiles of the following sample. 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32 Median in
11 s (Quartiles) Find the median and quartiles of the following sample. 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32 Q 1 Median Q 3 in
12 s in Definition (Five-number summary) five-number summary of a set of numbers consists of the five quantities Minimum 1 st quartile Median 3 rd quartile Maximum se five numbers divide the set of numbers into four groups of equal size, each containing one-fourth of the set.
13 s (Five-number summary) 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 in
14 Practice s Practice Find the five-number summary of the sample 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32, 35. in
15 s 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. y are the five-number summary. in
16 s Five-number summary Use the to find the five-number summary of the rainfall data in
17 Summaries and Distributions If the distribution were uniform from 0 to 10, what would be the five-number summary? s in
18 Summaries and Distributions If the distribution were uniform from 0 to 10, what would be the five-number summary? s 50% 50% Med in
19 Summaries and Distributions If the distribution were uniform from 0 to 10, what would be the five-number summary? s 25% 25% 25% 25% Q 1 Med Q 3 in
20 Summaries and Distributions Where would the median and quartiles be in this symmetric non-uniform distribution? s in
21 Summaries and Distributions Where would the median and quartiles be in this symmetric non-uniform distribution? s 50% 50% Med in
22 Summaries and Distributions Where would the median and quartiles be in this symmetric non-uniform distribution? 25% 25% 25% 25% s Q 1 4 Med 5 Q in
23 Summaries and Distributions Describe the distribution. s Min Q 1 Med Q 3 Max in
24 Summaries and Distributions Describe the distribution. s in Min Q 1 Med Q 3 Max
25 Summaries and Distributions Describe the distribution. s Min Q 1 Med Q 3 Max in
26 Summaries and Distributions Describe the distribution. s Min Q 1 Med Q 3 Max in
27 s Definition ( range) interquartile range, denoted IQR, is the difference between Q 3 and Q 1. IQR is a commonly used measure of spread, or variability. Like the median, it is not affected by extreme outliers. in
28 IQR (IQR) IQR of s in is 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32 IQR = Q 3 Q 1 = = 15
29 IQR (IQR) IQR of 5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32, 35 s in is IQR = Q 3 Q 1 = = 15
30 IQR s (IQR) IQR of the rainfall data is is IQR = Q 3 Q 1 = = 8.69 cm in
31 IQR s Practice Find the five-number summary and the IQR of the sample 5, 20, 30, 45, 60, 80, 100, 140, 175, 200, 240. Are the data skewed? in
32 Salaries of School Board Chairmen s in Practice Find the five-number summary of the following salaries of school board chairmen. County/City Salary County/City Salary Henrico 20,000 Caroline 5,000 Chesterfield 18,711 Louisa 4,921 Richmond 11,000 Powhatan 4,800 Hanover 11,000 Hopewell 4,500 Petersburg 8,500 Charles City 4,500 Sussex 7,000 Prince George 3,750 New Kent 6,500 Cumberland 3,600 Goochland 5,500 King & Queen 3,000 Dinwiddie 5,120 King William 2,400 Colonial Hgts 5,100 West Point 0
33 Summaries and Stem-and-Leaf Displays s in It is possible to use a stem-and-leaf display to find a five-number summary, especially if the leaves are arranged in order. Find a five-number summary of the following January rainfall data. Stem Leaf Note: 1 2 means 12.
34 s Definition of Percentile s in Microsoft s uses a definition of the p th percentile that is based on the gaps between the numbers rather than on the numbers themselves. Definition ( s p th percentile) s p th percentile of a set of numbers is the number whose rank (position) is given by ( p ) r = 1 + (n 1). 100 If r is not a whole number, then interpolate between values.
35 s Read Section , pages Work 5.4, page 314, as an exercise. in
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