1. Chapters 1, 2, & 3 Yellow Stickie Questions… …from 02/22/16

2. Mean versus Median… Let’s calculate the mean and the median for the following data sets: Example #1: 1, 1, 1, 2, 3, 3, 100 Example #2: 10, 10, 10, 10, 15, 20, 20, 20, 20 Example #3: 2, 500, 500, 501, 505, 515, 516

3. SampleStatistic (changes from sample to sample; can vary) PopulationParameter (is fixed; does not change) Examples include µ, p, σ Population parameter vs. Sample statistic …

4. Go to Math 140 data on my website. Select and copy into StatCrunch the ‘how much do you weigh?’ data How many students are in this data? Is every student that attends COC included in this data? Calculate the summary statistics for this distribution; compare & contrast sample statistics vs. population parameter

5. Population parameter vs. Sample statistic… The Department of Fish & Game are concerned about the health of fish in Lake Tahoe. They want some information about the weight of fish living in the lake. They go out on the lake on several randomly- selected days and catch (then release) about 20 fish each day at random locations in the lake and weigh each fish. They then calculate the mean and the standard deviation of the weights of the fish they caught

6. Population parameter vs. sample statistic… Let’s say that you are my population Raise you hand if you wear prescription glasses. The proportion of us who wear prescription glasses is p = _____ Now let’s say you are my sample… same question…

7. Shape, Outlier(s), Center, Spread… (SOCS) S – Shape.Symmetric? Skewed? Uni-Modal, bi- modal, tri-modal, multi-modal? Gaps? O– Outlier(s)Is/are there unusually large or small values that are “away” from the majority of the rest of the data? C – CenterMean or median; what is the “typical” value of the distribution/data? S – SpreadStandard deviation or inter-quartile range; typically/on average, how far apart or close together is the data/distribution?

8. SOCS & Math 140 Units Data… Let’s create a histogram & analyze through SOCS Let’s practice changing bin width Select to show mean and median on graph

9. SOCS & Math 140 Weight Data… Let’s create a histogram & analyze through SOCS Let’s practice changing bin width Select to show mean and median on graph

10. Which graph do I use? Dot plots, stem plots, histograms, box plots… when do we use these? How do we know which to use? Pie charts, bar graphs… when do we use these? How do we know which to use?

11. Which graph do I use? Dot plots, stem plots, histograms … USUALLY when distributions are symmetric or fairly symmetric Box plots… USUALLY when distributions are skewed (left or right), not symmetric How do we know which to use?

12. Which graph do I use? Dot plots, stem plots, histograms … USUALLY when distributions are symmetric or fairly symmetric; and USUALLY go with mean as measure of central tendency & standard deviation as measure of spread Box plots… USUALLY when distributions are skewed (left or right), not symmetric; and USUALLY go with median as measure of central tendency & inter-quartile range as measure of spread (more on this later in this chapter)

13. Standard Deviation… what is it anyway? Measures the spread of a distribution by looking at how far the observations are from their mean. How spread out is data? How condensed is data? Consider the data set 1, 1, 2, 3, 3 & the data set 1, 150, 400, 5000, 7900; which has the larger standard deviation?

14. Standard deviation… what is it anyway? Let’s calculate, by hand, the standard deviation for the distributions: 1, 2, 3AND1, 20, 45

15. First Distribution: 1, 2, 3

16. First Distribution: 1, 20, 45

17. Confounding variables… what the heck are they? A confounding variable is an extraneous (potentially unknown) variable in a statistical model that can effect a situation Example: Children who have higher IQ’s tend to have higher reading scores. So there is a positive association between children’s IQ’s and reading scores. So the reason why children have higher reading scores is because they have high IQ’s, right?

18. Confounding variables… what the heck are they? A confounding variable is an extraneous (potentially unknown) variable in a statistical model that can effect a situation Example: In the 1600’s rum imports to the colonies were increasing dramatically. At the same time, the number of Methodist ministers were as well. So the reason why rum imports were increasing was because of the increased amount of ministers. Right?

19. …that’s it …. Any other questions on Chapter 2? Let’s take the Chapter 2 HW quiz…