1. Samples and Populations
Making Comparisons and Predictions

2. Using Samples to Draw Conclusions
Investigation 3
Using Samples to Draw Conclusions

3. Homework
Page 69 A 1,3,4,5,8,12,14 B 1,3,4,5,7,12,13 IXL S7 and S8 solving equations and word problems

4. Vocab
Simulates Run an experiment that models the relevant characteristics Capture-tag-Recapture method one method to estimate a population, biologists capture a sample of deer in a specific area, tag the deer, and then release them, later they recapture another sample of deer and count the number of deer with tags and compare that number to the sample

5. Invest 3.1 Solving an Archeological Mystery Comparing Samples Using Box Plots
How might you analyze samples from known and unknown populations to determine whether the unknown population has one or more attributes in common with the know population?

6. Example 57
You need your book for this data, there is too much to copy to have in your sheet. A1. For each known site and each unknown site find the five number summary of the arrowhead-length data. Then draw a box and whisker plot of each distribution, we will divide into groups for this data A2. Using the data to compare the lengths of the arrowheads found at the unknown sites and the known sites a during which time period 4000bc to 500 ad or 500 ad to 1600 do you think site 1 was settled, explain 4000 to 500 very comparable data b. during which time period do you think site 2 was settled explain 500 to 1600 very similar data Suppose the archeologist had collected only a few arrowheads from each unknown site, might they have reached a different conclusion? might not be a good representation of the area, some of the samples were smaller but still yielded a good amount of data

7. Notes
IQR is the space of the box Each part of the box and whisker plot is 25% of the data Be able to compare data to help predict which area something belongs to, based on what you know The more data you can collect the better

8. Homework
You should be able to complete 1 and 2

9. Invest 3.2 Comparing Heights of Basketball Players Using Means and MADs
How can you determine whether differences in sample data are large enough to be meaningful, or just due to naturally occurring variability from one sample to another?

10. Example pg 61

11. Compare the means of the two sets of data and the MAD
Means are different by about 16, MAD’s are close by about 2
On each dot plot
a. Mark the mean
b. Mark 2 MAD’s less than and greater than the mean
3. For each distribution what percent of data is located within 2 MAD’s
Female 93% Male 90%

12. Do you think this random sample represent the heights of male or female players? Explain mean is and MAD is 7.64 closer to sample of male players

13. Notes
Be able to use the MAD data to help compare data on graphs Remembering that most of the data should be between 2 MADs from the mean Similar to the arrowheads – using the data we know to help predict new data

14. Homework
You should be able to complete 3-7

15. Invest 3.3 Five Chocolate Chips in Every Cookie Using Sampling in a Simulation
How do you simulate a real-world problem? How can you analyze the data that you collect from that simulation to draw conclusions?

16. Example pg 63
Read problem on page 63 Given the following picture How might you correct Jeff’s reasoning about how many chocolate chips to add to each batch of cookie dough? What advice would you give to Jeff and Hadiya to help them solve this quality-control problem?

17. 12 cookies Each time you select a number that puts a chocolate chip in that cookies, until you have 5 chips in each

18. What is the probability that a chip will be assigned to a cookie?
1/12
Describe a method that you can use to give each chip a cookie number, explain why you method makes it equally likely for each cookie to be assigned a chip
as long as all events are equally likely
3. What is the total number of chips needed?
4. Get data from each group of total number of chips
a. Make a histogram of the class data
b. Describe the histogram, how did you decide intervals
range and overall spread, is the data clustered, using a lot of chips would get you there by cookies could average 13 chips
c. Make a box and whisker plot – what does it tell you
where 50% of the data is located, look at range, IQR
d. Find the mean and median and compare
where mean and median are different

19. Notes
Using ideas of probability to simulate a situation Finding other methods that will give equally likely results one of everything in the sample Comparing Range, overall spread, clusters of data Histograms to set up frequency – depends on range of numbers Using different methods to predict mean and median Again about box and whisker 50% of data Look at the overlap of the box and whisker plots to compare data

20. Homework
You should be able to complete 8-10 and 30

21. How can you estimate the size of a large population?
Invest 3.4 Estimating a Deer Population Using Samples to Estimate the Size of a Population
How can you estimate the size of a large population?

22. Example pg 67
Simulation Beans – you have a container of beans and 100 of them are mark with a pen
Take a sample of 25 beans. Record the number of marked beans and the number of unmarked beans, then estimate the total number of beans, complete the table

23. 2. How did you estimate the total number of beans in the container?
set up a basic proportion
Why is this a simulation?
basic definition of what a simulation is
4. Get data from all groups for total number of beans for each sample space
for each sample size draw a line plot
How might the lines plots change you estimate for the total number of beans?
they give you more data to help give an estimate, look at mean or median

24. Notes
Capture-Recapture – to help determine size of large populations Remembering the definition of a simulation experiment that models the relevant characteristics Seeing that different representations of data and amounts of data can change your overall perspective and predictions

25. Homework
You should be able to complete and 29

26. Essential Questions
How might you analyze samples from known and unknown populations to determine whether the unknown population has one or more attributes in common with the know population? Look for similar characteristics, mean, median, mode, range, type of grapy How can you determine whether differences in sample data are large enough to be meaningful, or just due to naturally occurring variability from on sample to another? Look at a few sizes of the data and compare you m,m,m, and other types of data How do you simulate a real-world problem? How can you analyze the data that you collect from that simulation to draw conclusions? finding a model that simulates the situation and each outcome is equally likely How can you estimate the size of a large population? capture-recapture to record a sample set and then set up a proportion