1. Unit 8: Statistics Prof. Carolyn Dupee July 3, 2012

2. 8.1 STATISTICS TERMS Statistics- the art & science of gathering, analyzing, and making inferences (predictions) from numerical information (Data) obtained in an experiment. Population- all items or people of interest Sample- some of the items in the population used to make predictions. Unbiased sample- one that is a small replica of the entire population with regard to income, education, gender, race, religion, political affilation, age, etc. 2

3. (UNBIASED) SAMPLING TECHNIQUES SAMPLES): 1.random sampling- each time an item is selected in the population there is an equal chance of an item being drawn. 1.Usually numbers are randomly assigned using a calculator or computer program to ensure randomness. 2.Ex. Randomly select a tennis ball from a bag containing 300 balls. 3

4. (UNBIASED) SAMPLING TECHNIQUES 2. Systematic sampling- when a sample is obtained by drawing every nth item on a list or production line; first item should be determined by using a random number. -be careful that the entire population is considered. -Make sure that every nth item does not come from the same source such as the same machine creating it. 4

5. (UNBIASED) SAMPLING TECHNIQUES 3. Cluster sampling- random selection of a group of units or area sampling; divide into geographic areas and then select the sections or clusters. 4. Stratified sampling- divide the population by creating strata or parts such as by gender, race, religion, or income. 5. Convenience sampling- uses data that are easily or readily obtained; information from some people is better than none at all; Ex. People who return surveys are more interested in the question than those who do not. -Can be biased! 5

6. P. 333 EX. 1 IDENTIFYING SAMPLING TECHNIQUES: Identify the sampling technique used to obtain a sample in the following. Explain your answer. Every 20 th car coming off the assembly line is check for defects. A $50 gift certificate is given away at the Annual Bankers Convention. Tickets are placed in a bin, and the tickets are mixed up. Then the winning ticket is selected by a blindfolded person. 6

7. P. 333, EX. 1 Children in a large city are classified based on the neighborhood school they attend. A random sample of give schools is selected. All the children from each selected school are included in the sample. The first 50 people entering a zoo are asked if they support an increase in taxes to support a zoo expansion. Students at Portland State University are classified according to their major. Then a random sample of 15 students from each major is selected. 7

8. 8.2: MISUSES OF STATISTICS P. 336-7 vague or ambiguous words- - Ex. Average, largest stating a claim from which the public may draw irrelevant conclusions. -Ex. 212 people switched to insurance company Z. (omitted that 415 people dropped the insurance during the same period. Practice Exercises: p. 338-339 3-16 8

9. 8.3 FREQUENCY DISTRIBUTIONS Ex. 1 p. 341 The number of children per family is recorded for 64 families surveyed. Construct a frequency distribution of the following data. 01122345 01122346 01222346 01223347 01223348 01223358 01223359 9

10. FREQUENCY DISTRIBUTIONS Number of children (observed)Number of families (frequency) 08 111 218 311 46 54 62 71 82 91 10

11. RULES FOR DATA GROUPED BY CLASSES (p. 341) The classes should be of the same width. The classes should NOT overlap. Each piece of data should belong to only one class. 11

12. EX. 3 P. 344 The following set of data represents the family income (in thousands of dollars rounded to the nearest hundred) of 15 randomly selected families. Construct a frequency distribution with a first class of 16.5- 22.6. 31.516.830.829.725.9 50.237.429.638.7 33.8 20.525.324.841.335.7 12

13. STEP 1: PUT THE NUMBERS IN NUMERICAL ORDER. 16.825.329.733.8 38.7 20.525.930.835.741.3 24.829.631.537.450.2 13

14. STEP 2: CREATE A FREQUENCY TABLE IncomeNumber of Families 16.5-22.6 (given in question)2 22.7-28.83 28.9-35.05 35.1-41.23 41.3-47.41 47.5-53.61 Total15 14

15. QUESTIONS TO ANSWER What’s the modal class? (mode means number that shows up the most) 28.9-35.0 What’s the midpoint of the first class? (take the smallest and largest number and divide by 2) 16.5 + 22.6 = 19.55 2 Practice Exercises: p. 345 7-9; 11-18 15

16. CIRCLE GRAPHS (OUT 0F 100%) Ex. 1 p. 347: Six hundred people who attended a Ringling Brothers, Barnum & Bailey circus where asked to indicate their favorite performance. The results are shown below. PerformanceNumber of People Tigers230 Elephants154 Acrobats99 Jugglers91 Other26 600 16

17. CONSTRUCTING A CIRCLE GRAPH Performanc e # of People % of TotalM< of central angle Tigers230230/600X100=38.3%0.383X 360 o = 137.9 o Elephants154154/600X100= 25.7% 0.257X360 o = 92.5 o Acrobats9999/600X100= 16.5%0.165X360 o = 59.4 o Jugglers9191/600X100= 15.2%0.152X360 o = 54.7 o Other2626/600X100= 4.3%0.043X360 o = 15.5 o 17

18. HISTOGRAMS & FREQUENCY POLYGONS statistical graphs used to illustrate frequency distributions (either a bar graph or a line graph). -The first column is understood to be on the X-axis or horizontal axis. -The second column is understood to be on the Y-axis or vertical axis. -Make sure both axes are properly labeled and that numbers are appropriate. -Y-axis must go from 1 to a little higher than 18. 18

19. P. 348 EX. 2 CONSTRUCT A HISTOGRAM (BAR GRAPH) Number of ChildrenNumber of Families 08 111 218 311 46 54 62 71 82 91 19

20. P. 349 EX. 3 CONSTRUCT A FREQUENCY POLYGON (LINE GRAPH) Construct a frequency polygon of the frequency in Example 2. Use the same information from the question below, BUT make a dot at each point, and connect the dots. 20

21. P. 351 EX. 6 STEM-AND-LEAF DISPLAY The table below indicates the ages of a sample of 20 guests who stayed at Captain Fairfield House Bed and Breakfast. Construct a stem-and-leaf display. 562931394356 59586062595832 504727502871 7244454468 21

22. STEM-AND-LEAF PLOTS Put them in groups based on numbers. 20’s 29, 27, 28 30’s 31, 39, 32 40’s 43, 47, 44, 45, 44 50’s56, 59, 58, 5050’s56, 59, 58, 50 60’s60, 62, 68 70’s71, 72 22

23. STEM-AND-LEAF PLOTS Put all the tens on one side and all the ones on the other side in numerical order. 27 8 9 31 2 9 43 4 4 5 7 50 6 8 9 60 2 8 71 2 23