1. C HAPTER 3

2. 3-1 M EAN, M EDIAN, M ODE, AND R ANGE IWBAT compute the mean, median, mode, and range from a data set

3. V OCABULARY Mean – Average using division Median – Average using the central number Mode – Average using the number that occurs most frequently Range – How far is the data spread out Measures of Central Tendency – The mean, median, and mode. They indicate what is typical of a set of data.

4. M EAN Find the mean of the number of people at a play during 8 showings. 100, 100, 89, 90, 95, 100, 90, 104 1) Add all numbers in data set 100 + 100 + 89 + 90 + 95 + 100 + 90 + 104 768 2) Divide the sum by the number of data in the set 96 The Mean is 96

5. M EDIAN Find the median of the number of people at a play during 8 showings. 100, 100, 89, 90, 95, 100, 90, 104 1) Write data in order from least to greatest 89 90 90 95 100 100 100 104 2) Starting from opposite ends, find the number(s) in the middle *If there are two numbers left in the middle: find the mean of the two numbers

6. M ODE AND R ANGE Find the mode of the number of people at a play during 8 showings. 100, 100, 89, 90, 95, 100, 90, 104 1) Mode: Which number(s) occur the most frequently 100 2) Range: Subtract lowest number and the greatest number 104 – 89 = 15 Mode: 100 Range is 15

7. E XAMPLES Find the mean, median, mode and range of the following data set. 31, 25, 37, 25, 42 1) Mean 31 + 25 + 37 + 25 + 42 160 32 2) Median25 25 31 37 42 31 3) Mode 25 4) Range42 – 25 = 17

8. I NDEPENDENT P RACTICE Find the mean, median, mode, and range of the following data set. 35, 20, 7, 12, 35, 12, 9, 6

9. 3-2 D ATA WITH O UTLIERS IWBAT compute the mean, median, mode, and range of data sets with and without outliers to determine their effect on central tendencies

10. V OCABULARY Outlier – A number in a data set that is very different from the rest of the numbers. Data sets can have more than one outlier.

11. I DENTIFY THE OUTLIERS. T HEN F IND THE MEAN, MEDIAN, AND MODE WITH AND WITHOUT THE OUTLIERS. R OUND MEAN TO THE NEAREST TENTH. 15, 18, 12, 9, 46 1) Identify the outlier(s)46 2) Find mean, median, mode with outlier = 20 Median: 9 12 15 18 46 15 Mode: None

12. 3) Find mean, median, and mode without the outlier = 13.5 Median: 9 12 15 18 = 13.5 Mode: None *How did the outlier effect the mean? (Increase or decrease) The mean was increased by the outlier *How did the outlier effect the median? The median was increased by the outlier

13. E XAMPLE Identify the outliers. Then find the mean, median, and mode of the data with and without the outlier. Round the mean to the nearest tenth. Outliers 25, 33, 28, 14, 35, 60 14 and 60 With outliers Mean: 25 + 33 + 28 + 14 + 35 + 60= 195 = 32.5 Median: 14 25 28 33 35 60 28 + 33= 61= 30.5 Mode: None

14. Without outliersMean: 25 + 33 + 28 + 35= 121 = 30.25 Median: 25 28 33 35 28 + 33= 61= 30.5 Mode: None *How did the outliers effect the mean? (Increase or decrease) The mean increased with the outliers *How did the outliers effect the median? The median was not effected by the outliers *How did the outliers effect the mode? The mode was not effected by the outliers

15. 3-3 S TEM - AND -L EAF P LOTS IWBAT use stem-and-leaf plots to analyze central tendencies of data with 2 or 3 digit numbers

16. M AKING A S TEM - AND -L EAF P LOT Average Olympic Basketball Scores AngolaArgentinaAustraliaBrazilChinaCroatia 567096927285 GreeceLithuaniaPuerto Rico South Korea USAYugoslavi a 8085898110496 1)Make a stem-and-leaf plot of the data 2)Use the stem-and-leaf plot to find the range, median, and mode.

17. E XAMPLE Albuquerque 75 Flagstaff 60 Missoula 59 Salt Lake City 67 Bismarck 65 Fort Worth 82 Portland 64 San Francisco 61 Boise 66 Lincoln 73 Rapid City 65 Seattle 60 1)Make a stem-and-leaf plot of the data. 2)Use the stem-and-leaf plot to find the range, median, and mode.

18. U SING A S TEM - AND -L EAF P LOT Average Yearly Precipitation in Some US Cities (in Inches) StemLeaf 4545 1 1 2 3 5 7 1 4 4 1)Find the Range 2)Find the Median 3)Find the Mode

19. E XAMPLE Heights of Buildings Downtown (in feet) StemLeaf 2 3 4 5 6 7 8 9 10 11 12 55 8 8 9 25 5 9 0 2 3 8 2 34 7 8 5 0 1 4 4 7 8 35 9 58 6 1)Why is the leaf of stem 6 blank? 2)Find the range 3)Find the mode

20. 3-4 C HOOSING THE B EST G RAPH IWBAT choose the type of graph that best describes a set of numerical data and relationships.

21. T YPES OF G RAPHS Bar Graph – shows specific number of multiple groups (ex. Number of students in each class) can also use a pictograph Double Bar Graph – compares and contrasts two groups side-by-side (ex. Sports that girls play vs. sports that boys play) Line Graph – shows changes over time or other kinds of interrelationships (Ex. Temperatures over a month, Population over several years) Circle Graph – Describes parts of a whole (Ex. The percentage of students that like specific types of music)

22. E XAMPLES Community Theater Group Year# of Dramas# of ComediesAttendanceCost per Ticket 19961086,500$10.50 19971574,000$12.00 19981295,500$12.50 199912108,000$14.00 1) Which sets of data show totals for each year? Number of dramas, number of comedies, and attendance 2) Which set of data shows a steady increase over time? Cost per ticket 3)Which type of graph would be best for the data on the number of dramas and number of comedies? Why? Double bar graph, compares the specific numbers of two groups

23. 4)Which type of graph would be best for the data on cost per ticket? Why? Line graph, shows change of prices over several years

24. W HICH G RAPH S HOULD Y OU U SE ? 1) You want to show that the music store sells about 4 times as many country music CDs as jazz CDs. Bar Graph or Pictograph 2)You want to show that sales at the music store have been falling steadily for the last three years. Line Graph 3)You want to show that current sales of Elvis’ recordings are greater than sales of the Beatles’ recordings. Bar Graph or Pictograph 4)You want to show what part Oldies and Classic Rock CDs are of the entire collection of music in the store. Circle Graph

25. 3-5 U NDERSTANDING S AMPLING IWBAT understand the use of sampling in describing group tendencies.

26. V OCABULARY Population – The entire group of people or things being considered (Ex. All students at Holy Angels, The entire bag of marbles) Sample – Part of the population (Ex. Girls at Holy Angels, Only the 6 th grade class, A handful of marbles from the bag) Samples are used when studying or surveying when the population is too difficult or impractical

27. E XAMPLE #1 There is a barrel of marbles. You want to know how many green marbles are in the barrel. You scoop out a bucket of marbles. 1) What is the population?The whole barrel of marbles. 2) What is the sample?The bucketful of marbles. You want to take two samples to estimate a central tendency. Sample 1: There are 210 marbles in the bucket. Of those marbles, 51 are green. 1) Find the percentage 24%

28. Sample 2: You scoop another bucketful. This time there are 188 marbles, 61 of those are green. 2) Find the percentage 32% 3) Compare both samples by finding the mean 24% and 32% 4) Round (make the number end with a zero or a 5) About 30% of the barrel is green

29. E XAMPLE #2 In each situation, would it make more sense to study the entire population or a sample? David got a new shipment of dog treats. Each small bag is supposed to contain pieces of real beef jerky. David wants to know the mean number of pieces of beef jerky per bag. It would take too long to count jerky in all the bags, so it’s best to take a sample from one or two bags.

30. E XAMPLE #3 Kristen wants to know the mean height of her cat’s new kittens. A cat can only have so many kittens. It won’t be terribly difficult measuring a few cats that live in the house, so you can study the entire population.

31. E XAMPLE #4 Dog Owners BreedPercent Beagle35% German Shepherd30% Retriever25% Other10% The table shows the results of a poll in 1999 of 500 dog owners in a large city. Were the statistics drawn from a sample or from the entire population? The population is all the dog owners in the city. Is it possible to poll every single owner? No, it even tells you that only 500 dog owners were polled.

32. 3-6 S AMPLING M ETHODS IWBAT understand how the method of sampling determines how representative the sample is of the population.

33. V OCABULARY Biased – A sample that does not mirror the population. Random Sampling – A sample where each person or thing has an equal chance of being chosen. Representative – A sample that mirrors the population. Convenience Sampling – Any convenient method to use to choose the sample. Responses to a Survey – A form of sampling where you ask people to take a survey. Tends to be biased since those with strong opinions are more likely to take a survey.

34. E XAMPLE #1 Cassie wants to determine which brand of athletic shoes is most popular with U.S. middle school students. She decides to stand near the entrance of the school and keep a count of what brands of shoes students are wearing when entering the school. 1. What sampling method is Cassie using? How do you know? Convenience Sampling because she’s going to her own school. 2. Is it likely to be representative or biased? Explain. Biased because she is only studying the students at her school and not at any other schools.

35. M ORE E XAMPLES Tell whether each sample is likely to be representative or biased. Explain your answers. Identify each as random sampling, convenience sampling, or responses to a survey. 1. A state legislator mails questionnaires about literacy to all the eligible voters in her district. Only 12% of the people return the questionnaire. Biased because people who are illiterate won’t be able to read the questionnaire. This is responses to a survey. 2. A school principal questions every student whose locker number ends in a 9 to gather student input about plans for the new library. Representative because students of different grade levels and interests would be studied. This is random sampling.

36. 3-7 M AKE A G RAPH IWBAT make graphs to illustrate data and solve problems.

37. 3-8 A NALYZING S TATISTICAL R ESULTS IWBAT evaluate the effect of questions on statistical results.

38. 3-9 R EPRESENTING A P OINT OF V IEW IWBAT analyze data displays and evaluate the influence of the display on the conclusions.