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Statistics Unit

Statistics Unit. Lesson 1: Collecting Data.

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Statistics Unit

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  1. Statistics Unit Lesson 1: Collecting Data

  2. Statistics Lesson 1: Collecting Data Learning Targets:I know the meaning of “a sample from a population” and “a census of a population”. (S3.1.1)I can distinguish between sample statistics and population parameters. (S3.1.1) I can use samples to make inferences about populations and determine relationships and interpret data. (S3.1.1)I know the effect of replication on the precision of estimates. (S3.1.2) I can identify possible sources of bias in data collection and sampling methods and simple experiments. (S3.1.2)I can explain the impact of bias on conclusions made from analysis of data (margin of sampling error) (S3.1.2)

  3. Statisticsbranch of math dealing withcollection, organization, analysisand interpretation of information calleddata

  4. Consider this situation: The medical lab tech gets an order for counting the number of white blood cells in a patient’s blood. The “variable” is what mightvary. It’s what can beclassifiedorcountedor measured. In this case ex., the number of white blood cells. The “population” is the set of all objectsyou want to study. In this case, the population is “all the patient’s blood.”

  5. Consider this situation: The medical lab tech gets an order for counting the number of white blood cells in a patient’s blood. If the lab tech takes out all the patient’s blood to analyze it, the patient will die. This is not what the lab tech wants. So she decides to use a “sample”. A“sample” is the part of thepopulation you can actually study. In this case, the sample is taking out “some” of the patient’s blood.

  6. Example 1: The Student Senate is counting the number of students wearing black and white for Spirit Week. There are 2200 total students enrolled at West Ottawa High School. The Student Senate President counts the number of students wearing black and white in a randomly selected classroom containing 30 students. Population?________________ Sample? _________________ Variable? ___________________

  7. Consider this situation: The medical lab tech gets an order for counting the number of white blood cells in a patient’s blood. Sometimes statisticians are not in the medical field. A political scientist might want to know what people think of a health care issue like giving swine flu immunizations. In this case, taking blood won’t cut it. Survey:give a questionnaire or gather answers to a question in an interview. census:complete listof all the values in a population (ex., US Census)

  8. Random Samples Samples can be taken randomly, in a way so that every member of the population has an equal chance of being chosen. In our example, the blood draw would be of random blood cells. This will enable us to estimate information about the population.

  9. Bias If a sample is not chosen randomly from a population, the data from the sample may not apply to the population. If a sample isnot random, and therefore not representative of the population, it is said to be biased.

  10. Example 2:Determine whether each situation would produce a random sample. Write yes or no and explain your answer.a. surveying of students at the prom of whether or not they like to danceb. polling every 5th person who walks into the mall about what is their favorite color

  11. Margin of Sampling Error If the percent of people in a sample responding in a certain way is p and the size of the sample is n, then 95%of the time, the percent of the population responding in that same way will be between p - MEand p + ME, where

  12. Example 3: In a survey of 120 randomly selected students, 37% answered “yes” to lying to their parents in the past week. What is the margin of error? What does the margin of error mean? This margin of error means that with _____% accuracy the actual percent of people who had lied to their parents in the past week is between _____% and _____%.

  13. Your Turn 3: In a survey of 240 randomly selected adults, 85%answered “no” to smoking in the past week. What is the margin of error? What does the margin of error mean? This margin of error means that with _____% accuracy the actual percent of people who had not smoked cigarettes in the past week is between _____% and _____%.

  14. Example 4: In a survey, 30% of the people surveyed said they had smoked cigarettes in the past week. The margin of error was 2%. How many people were surveyed? 1) Substitute #s into the equation NOTE: ME as a decimal 2) Solve for n: i) divide by 2 ii) square both sides iii) mult. both sides by n iv) divide by the ME value

  15. I can use samples to make inferences about populations and determine relationships and interpret data. (S3.1.1) Your Turn 4: In an earlier survey, 32% of the people surveyed said they did not complete all their math homework the past week. The margin of error was 4.5%. How many people were surveyed?

  16. Statistics: Collecting Data replication: Capture-recapture method: • capture, tag and release • Recapture and count The repetitionof an experiment or observation in the same or similar conditions. Replication adds information about the reliability of conclusions to be drawn from the data.

  17. Example 5: In order to estimate the number of salmon in Little John Lake, L.J. captured and carefully tagged 62 salmon. He then released them. The next month, he caught 149 salmon, of which 23 were tagged. About how many salmon were in the lake?

  18. I know the effect of replication on the precision of estimates. Your Turn 5: In order to estimate the number of perch in Sapphire Lake, Tim captured and carefully tagged 23 perch. He then released them. The next month, he caught 62 perch, of which 14 were tagged. About how many perch were in the lake?

  19. Assignment: Worksheet 1

  20. I can use samples to make inferences about populations and determine relationships and interpret data. (S3.1.1) Warm-Up: Health In an earlier survey, 25% of the people surveyed said they had exercised in the past week. The margin of error was 3%. a. What does the 3% indicate about the results?This margin of error means that with _____% accuracy the actual percent of people who had exercised in the past week is between _____% and _____%. b. How many people were surveyed?

  21. Statistics Lesson 2: Tables, Bar Graphs, and Circle Graphs Learning Targets:I can read and interpret tables, bar graphs and circle graphs. (S1.1.1)I can draw graphs to display data. (S1.1.1)

  22. Example 1:Table Graph

  23. Pie Charts/Circle Graphs Ex 2 Circle Graphs Using your knowledge of a circle, what percent do you think answered “yes” to the question of having uniforms at school? Either “no or unsure”? “Unsure” alone?

  24. Your Turn 2 Circle Graphs

  25. Bar Graphs: • One axis labels categories or variables • The other axis usually a numerical scale • Categories are identified and labeled • A legend often given for clarity • 5. In order to portray relations between data accurately, numerical scales should begin with zero

  26. Example 3: Horizontal Bar Graph:

  27. Your Turn 3: Bar Graph - Multiple Bars

  28. Statistics Lesson 3: Other Displays Learning Targets:I can calculate measures of spread for data sets. I can use statistics to describe data sets or to compare and contrast data sets. I can read and interpret bar graphs and coordinate graphs. I can draw graphs to display data.

  29. 3: Other Displays Check out the scales on the graphs. Which give a more accurate picture of the rat of change of the population? Why?

  30. Average Rate of Change: Average rate of change is the slope of the segment.

  31. Slopes on Intervals: positive slope on an interval negative slope on an interval zero slope on an interval

  32. Slopes on Intervals

  33. Example (Back to Boston from example 1) Calculate the average rate of change in the population of Boston in the time interval: between 1850 and 1900 between 1950 and 1960

  34. Stem & Leaf: Similar to a bar graph (stems are like categories and the number of leaves is the number of grades in that category.) But, better than a bar graph, the individual data values are not lost. The value 68 is circled. • For example, you can clearly see the following: • maximum • minimum • range (difference between highest and lowest) • clusters (bunches of similar scores) • - outliers (scores very different from the rest)

  35. Back to Back Stem & Leaf: range # students # in 80s outliers?

  36. Closure (Lesson 3) The chart above shows daily temperatures in New York City. a. What is the average rate of change between day 2 and day 3? Is that interval increasing or decreasing? b. What is the average rate of change between day 5 and day 6? Is that interval increasing or decreasing?

  37. Assignment Worksheet 3

  38. I can read and interpret circle graphs. Warm-Up The pie chart above shows the ingredients used to make a sausage and mushroom pizza weighing 1.6 kg. • a. What ingredient was used the least? • b. How much cheese was used to make the pizza? • c. How much sausage was used to make the pizza?

  39. I can draw graphs to display data. Warm-Up • Make a stem and leaf plot showing the day of the month class members were born (Ex: December 17 would be a “17”.) • Write your “date” on the post-it as 7 and put it on the screen • (in the correct location). • 0 • 1 • 2 • 3 • Then find the maximum, minimum, and range of the data.

  40. Statistics Lesson 4: Measure of CenterI can calculate measures of center for data sets. (S1.2.1) I can use summation notation to represent a sum or mean. (intro) (S1.2.3)I can describe relations between measures of center. (S1.1.1)I can use statistics to describe data sets or to compare or contrast data sets. (S1.2.1)

  41. Measures of Center: measures of center measures of central tendency numbers that describe typical values in a data set

  42. Mean mean = arithmetic average the sum of the data divided by the number of items in the data set Example? my bank account over the months of June $450 July $275 August $400

  43. Median median = middle value of a set of data placed in increasing order Example same bank account: $450, $275, $400 What if the data set has an even number? 25, 30, 40, 52 Take the average of the two middle numbers!

  44. Mode mode = the most common item in the data set mode is always a member of the data set Mode is not considered to be a measure of center of a data set because it could be an extreme value.

  45. Back to Back Stem & Leaf

  46. Calculator Steps Find the STAT button. input list of data easiest to use default lists STAT-->Calc--->1-var stat ENTER

  47. Wacky Widget Company Enter lists and use your calculator to find the mean and median salary. (or do it by hand!) Mean salary: Median salary:

  48. Mean? Median? Mode ? Which measure would be most meaningful in each situation? a tailor stocking shirts a teacher looking at exam results a city council member budgeting local income tax

  49. Sigma Notation: The sum of the x-sub-i’s as i goes from a to b. i = index (It indicates the position of a number in an ordered list.) a = first number to evaluate b = last number to evaluate

  50. Sigma Notation Problems: Evaluate the following:

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