1 / 217

Statistics and Probability

Statistics and Probability. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation.

johnna
Download Presentation

Statistics and Probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

  2. Daily Questions 1.) A box company wants to make a cardboard box with a volume of 160 cubic inches. What are the dimensions of the box that will require the least amount of cardboard? 2.) Solve for x: 8(5 – 3)2 + x = 46 4 3.) A movie sold for $18 when it was first released. It is now selling for $12. By what percent has the price changed?

  3. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center What are they? Why do we use them? Why do we need all three?

  4. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center Find the mean, median, and mode of each data set. 46, 35, 23, 37, 29, 53, 43 Mean: Median: Mode: 72, 56, 47, 69, 75, 48, 56, 57 Mean: Median: Mode:

  5. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center The values in a data set are: 12, 8, 9, 5, 9, 8, 5, 10, 8, 6 Answer: 8 What was the question?

  6. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center The values in a data set are: 10, 7, 9, 5, 13, 10, 7, 14, 8, 11 Answer: 9.5 What was the question?

  7. Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

  8. Daily Questions 1.) Josh’s test scores were 95, 89, 87, 95, 86, and 88. Which measure of center will give Josh the highest final grade? 2.) The school librarian tracked how many books were checked out each day during a one-week period. Which of these measure of center is most affected by the number of books that were checked out on Wednesday? 3.) The distance from Wilmington to Los Angeles, CA on a map is 44 cm. The scale on the map is 1 cm = 50 mi. If you traveled an average of 60 mph for the entire trip, how much driving time would it take to get to Los Angeles?

  9. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Test Scores 88, 94, 90, 85, 88, 94, 79, 94, 88, 24

  10. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Concession Stand Soft Drink Purchases 2.00, 1.00, 2.00, 1.50, 2.00, 1.50, 2.00, 2.00, 1.00, 1.50, 2.00, 2.00, 2.00, 1.00, 2.00 (Lg: $2.00; Med: $1.50; Sm: $1.00)

  11. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Middle School Student Ages 10, 11, 12, 12, 14, 11, 12, 10, 11, 14, 13, 13, 14, 14, 12, 10, 12, 11, 12, 11, 13, 14, 14, 13, 10

  12. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Measures of Center: Which best represents the data? Meanis preferred… • most often • when an average is desired Median is preferred… • when you know that a distribution is skewed • when there is an outlier • when you have a small number of subjects Modeis preferred… • rarely • when describing discrete categorical data

  13. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Think-Pair-Share: Which measure of center would you use to BEST represent the data? Ages of Lions at Zoo 18, 4, 3, 7, 1, 6, 5, 4

  14. I can define and calculate the three measures of center. I can determine which measure of center best represents the data. Exit Slip 1.) Which measure of center for the following data set has the largest value? 33, 19, 28, 13, 18, 35, 33, 18, 25, 18 2.) The mean of a data set of 4 numbers is 5. The mean of a different data set of 10 numbers is 12. What is the mean of the combined data sets? 3.) Explain what would you do in the following situation: Mr. Hale gives you 3 minutes to find the average height of 7th graders at WMS. You have a list of all 7th graders and their heights.

  15. Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

  16. I can define and calculate the three measures of center.I can determine if a sample represents a population. Daily Questions 1.) What is the value of x? 2.) Find the three measures of center for the number of letters in each word of this question. 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8 Mean: Median: Mode:

  17. Today’s Lesson Learning Targets: I can define and calculate the three measures of center.I can determine if a sample represents a population. Standards of Mathematical Practices: 1, 2, 3, & 4 Your Responsibilities: - Read carefully - Share responsibilities - Collaborate - Answer completely

  18. Learning Targets: I can define and calculate the three measures of center.I can determine if a sample represents a population. New Vocabulary: Sample – A part of the population Population– The entire group of objects or individuals in a data set Your Responsibilities: - Read carefully - Share responsibilities - Collaborate - Answer completely

  19. Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

  20. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Daily Questions 1.) Kellogg’s receives a complaint about one of their cereals. Their taste testing team decides to sample their recent production by testing the first 100 boxes off the production line. Did the team’s sampling method accurately represent the population? Explain. 2.) To improve their sampling method, Kellogg’s decides to test the first 200 boxes off the production line. Is this sample better representing the population? Explain. 3.) A coffee shop manager in Dayton surveys his customers to see what percentage of Dayton residents drink coffee. According to his results, the manager concludes that 98% of Dayton residents drink coffee. Is the manager’s conclusion accurate? Explain.

  21. Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

  22. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Daily Questions 1.) Tina is a soccer player and wants to find out what percentage of her grade enjoys sports. She asks 12 people sitting at her lunch table to answer her survey. Identify all of the flaws to Tina’s surveying strategy. 2.) Solve for x: 7(8 – x) – 6 = 1 3.) What is the slope (unit rate) of this line? Dollars Paid (Hundreds) Hours Worked

  23. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Sleep/Movies Data Samples Student 1: Summarize your method of sampling the data, including sample size. Student 2: Explain your reasoning for choosing this method, including sample size. Student 3: Provide your results and discuss the math involved in finding that value.

  24. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Your task is to count the number of whales in the ocean or the number of squirrels in a park. How could you do this? What problems might you face? A sample is used to make a prediction about an event or gain information about a population. A whole group is called a POPULATION. A part of a group is called a SAMPLE.

  25. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A sample is considered random (or unbiased) when every possible sample of the same size has an equal chance of being selected. If a sample is biased, then information obtained from it may not be reliable. Example: To find out how many people in New York feel about mass transit, people at a train station are asked their opinion. Is this situation representative of the general population? No. The sample only includes people who take the train and does not include people who may walk, drive, or bike.

  26. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Food services at your school wants to increase the number of students who eat hot lunch in the cafeteria. They conduct a survey by asking the first 20 students that enter the cafeteria to determine the students' preferences for hot lunch. Is this survey reliable? Explain your answer. A Yes B No

  27. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. The guidance counselors want to organize a career day. 
They will survey all students whose ID numbers end in a 7 
about their grades and career counseling needs. Would this 
situation produce a random sample? Explain your answer. A Yes B No

  28. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. The local newspaper wants to run an article about reading habits in your town. They conduct a survey by asking people in the town library about the number of magazines to which they subscribe. Would this produce a random 
sample? Explain your answer. A Yes B No

  29. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. How would you estimate the size of a crowd? What methods would you use? Could you use the same methods to estimate the number of wolves on a mountain?

  30. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. One way to estimate the number of wolves on a mountain is to use the CAPTURE - RECAPTURE METHOD.

  31. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Suppose this represents all the wolves on the mountain.

  32. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Wildlife biologists first find some wolves and tag them.

  33. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Then they release them back onto the mountain.

  34. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. They wait until all the wolves have mixed together. Then they find a second group of wolves and count 
how many are tagged.

  35. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Biologists use a proportion to estimate the total number of wolves on the mountain: tagged wolves on mountain tagged wolves in second group total wolves on mountain total wolves in second group For accuracy, they will often conduct more than one recapture. = 8 2 w 9 2w = 72 w = 36 = There are 36 wolves on the mountain

  36. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Try This: Biologists are trying to determine how many fish are in the Rancocas Creek. They capture 27 fish, tag them and release them back into the Creek. 3 weeks later, they catch 45 fish. 7 of them are tagged. How many fish are in the creek? There are 174 fish in the river 27 7 f 45 27(45) = 7f 1215 = 7f 173.57 = f =

  37. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. A whole group is called a POPULATION. A part of a group is called a SAMPLE. When biologists study a group of wolves, they are choosing a sample. The population is all the wolves on the mountain. Population Sample

  38. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Try This: 315 out of 600 people surveyed voted for Candidate A. How many votes can Candidate A expect in a town with a population of 1500?

  39. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. 860 out of 4,000 people surveyed watched Dancing with the Stars. How many people in the US watched if there are 93.1 million people?

  40. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000.

  41. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect?

  42. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. The chart shows the number of people wearing different types of shoes in Mr. Thomas' English class. Suppose that there are 300 students in the cafeteria. Predict how many would be wearing high-top sneakers. Explain your reasoning. Shoes Number of Students

  43. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Sampling Practice Worksheet

  44. Statistics and Probability I can define and calculate the three measures of center. I can determine which measure of center best represents the data. I can determine if a sample represents a population. I can explain how random sampling produces a more accurate representation. I can use random samples to draw conclusions about a population.

  45. I can determine if a sample represents a population. I can use random samples to draw conclusions about a population. Daily Questions 1.) 10 large mouth bass are caught, marked, and released back into the pond. A few days later, 14 large mouth bass are caught, 4 of them marked. What is the estimated population of large mouth bass in the pond? 2.) Simplify: –21 – (–5) + (–2)³ 3.) Mark works 48 hours and earns $432. Cindy works for the same company, working 56 hours. She earns $512. Is this a proportional relationship?

  46. Measures of Variation - Vocabulary Review Range - The difference between the greatest data value and the least data value Quartiles - are the values that divide the data in four equal parts. Lower (1st) Quartile(Q1) - The median of the lower half of the data. Upper (3rd) Quartile(Q3) - The median of the upper half of the data. Interquartile Range - The difference of the upper quartile and the lower quartile. (Q3 - Q1) Mean absolute deviation - the average distance between each data value and the mean.

  47. Box-and-Whisker Plots

  48. Vocabulary • Box and Whisker Plots – a plot that uses a number line to show the distribution of a set of data • Lower Quartile – the median of the lower half of data • Upper Quartile – the median of the upper half of data • Interquartile Range – the difference between the lower and upper quartiles

  49. Why use a Box-and-Whisker?? • To analyze how data in a set are distributed • To compare two sets of data

More Related