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# Lecture 10.1 10.2 bt

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### Lecture 10.1 10.2 bt

1. 1. Today’s Agenda  Attendance / Announcements  Collect Projects  Note about Final Exam  Return Exams  Remaining Schedule  Sections 10.1, 10.2
2. 2. Exam Schedule  Exam 5 (Ch 10) Thur 12/5  Final Exam (All) Thur 12/12
3. 3. Intro to Statistics Statistics is the science that deals with the collection and summarization of data. Methods of stat analysis allow us to make conclusions about a population based on sampling. Statistics is more a field of Communications, than one of Mathematics!
4. 4. Intro to Statistics 1. 2. 3. 4. 5. Organize Data Display Data Identify the “averages” of the data Identify the “spread” of the data Make conclusions
5. 5. Obtaining Data • Want to represent a Population • Collect data from a Sample –Should be a Random Sample to be a fair representation of the population
6. 6. Tuition for a random sample of 30 private, 4-year colleges (thousands) 23 15 21 39 24 22 26 36 17 27 38 23 36 27 22 25 24 28 24 24 11 37 18 10 28 16 18 9 32 39
7. 7. 23 15 21 39 24 22 26 36 17 27 38 23 36 27 22 25 24 28 24 24 11 37 18 10 28 16 18 9 32 39 There are 30 Data Items, so n = 30 Where each can be called x i So, x4 25 “21”, “37”, etc. are Data Values
8. 8. Organizing Data • Frequency Distribution Table – Organize data into Classes • Usually between 5 - 15 – Each class must have the same Class Width Class width* = Max data value – Min data value Number of classes *Round up to nearest integer
9. 9. Organizing Data Let’s make a Freq. Dist. Table with 7 classes to organize the tuition data…Need Class Width! 39 9 CW * 7 So, each class will have a class width of 5! 4.28
10. 10. Organizing Data Make this column first! Note: Class width is not (9 – 5)!!! It is the distance between the lower limit of each class.
11. 11. Displaying Data 1. An account ing firm select ed 24 complex t ax ret urns prepared by a cert a in t ax preparer. T he number of errors per ret urn were as follows. Group t he dat a int o 5 classes, and make a frequency t able and hist ogram/ polygon t o represent t he dat a. Your Class Widt h = 8 12 0 6 10 8 0 14 8 12 14 16 4 14 7 11 9 12 7 15 11 21 22 19
12. 12. Displaying Data • Frequency Histogram (bar graph) – Each class is its own “bar” • No spaces between classes (bars) – Must label each axis (classes vs. frequency) – Use straightedge to make lines
13. 13. Tuition 35-39 30-34 25-29 20-24 15-19 10-14 5-9 frequency 9 8 7 6 5 4 3 2 1
14. 14. Displaying Data • Frequency Polygon (line graph) – Connects the midpoints of the top of each class. – Then connect to ground on each side – Use straightedge to make lines
15. 15. Tuition 35-39 30-34 25-29 20-24 15-19 10-14 5-9 frequency 9 8 7 6 5 4 3 2 1
16. 16. Characterizing Data
17. 17. Displaying Data 1. An account ing firm select ed 24 complex t ax ret urns prepared by a cert a in t ax preparer. T he number of errors per ret urn were as follows. Group t he dat a int o 5 classes, and make a frequency t able and hist ogram/ polygon t o represent t he dat a. Your Class Widt h = 8 12 0 6 10 8 0 14 8 12 14 16 4 14 7 11 9 12 7 15 11 21 22 19
18. 18. 10.2 Measures of Central Tendency • Ways to describe “on average…” – Mean • What is commonly thought of as “average” – Median • The “middle” of the data – Mode • The data value that occurs most often
19. 19. We need some data… • Number of hits during spring training for 15 Phillies players: (alphabetical order) 21 19 10 1 6 28 32 11 2 15 2 17 21 29 21
20. 20. Sample Mean • The mean of a sample set of data The sum of all data values “x bar” is the sample mean. Round to nearest hundredth. (2 decimal places) x x n The number of data items
21. 21. • Number of hits for 15 Phillies players: 21 19 10 1 6 28 32 11 2 15 2 17 21 29 21 x x n 21 19 15 21 15 .67
22. 22. Median • The “middle” of an ordered data set – Arrange data in order – Find middle value position n 1 2 • If n is odd, simply select middle value as the median. • If n is even, the median value will be the mean of the two central values (since a “middle” does not exist)
23. 23. Median Find the median for each data set. Age (years) in the intensive care unit at a local hospital. 68, 64, 3, 68, 70, 72, 72, 68 Starting teaching salaries (U.S. dollars). \$38,400, \$39,720, \$28,458, \$29,679, \$33,679
24. 24. Median • When is median a better indicator of “average” than the mean?
25. 25. Mode • The data value that appears most often – Single Mode • One data value appears more than any other – No Mode • No data values repeat – Multi-Mode • There is a “tie” for the value that appears the most
26. 26. Mode • Mode of Phillies data? • 2, 3, 3, 3, 5, 6, 6, 6, 7, 7, 10 • 18, 34, 61, 62, 85 • 9.5, 9.2, 9, 9, 9.1, 8.9
27. 27. Classwork / Homework • Page 604 • 1, 7, 21 – 25 • Page 614 • 1 – 19 odd, 29