Statistics

Unit 1:Probability distribution 

1. Generate appropriate methods for gathering representative samples (simple random sample(SRS), stratified sample, cluster sample, systematic sample)

2. Recognize bias and criticize it by describing how it overrepresents or underrepresents a segment of the population. Propose ways to reduce or eliminate bias.

3. Identify the sample and population in observations and experiments.

4. Recognize the purposes of and distinguishing features between observational studies and experiments.

5. Experiments have random assignments to treatments; observational studies simply observe subjects.

6. Observations can reveal associations; experiments can determine causation.

7. Observations are highly susceptible to confounding variables.

8. Observations might be conducted instead of observations for the sake of time, money, or ethics.

9. Experiments can use blocking, blindness, and/or placebos to strengthen the reliability of the results.

10. Generate an observational study or experiment to study a research question.

11. In an experiment, identify treatments, explanatory variable, response variable, and control.

12. In observational studies, identify explanatory variables, response variables, and confounding variables.

13. Confounding variables are hidden/sneaky variables that are related to both the explanatory and response variables, and they might be the actual variable behind the change in a response variable, rather than the explanatory variable.

14. Define, identify, and explain how blocking (including matched pairs blocking), placebos, and blindness (single and double-blind) can strengthen experiments.

1. Unit 2:Percentiles and normal curve

   1. Determine whether a variable is categorical, discrete quantitative, or continuous quantitative

   2. Be able to read & highlight info from pie charts, bar graphs, frequency tables, & relative frequency tables

   3. Be able to produce pie charts, bar graphs, frequency tables, & relative frequency tables from a list of data

   4. Be able to highlight info from stem-and-leaf plots, box-and-whisker plots, dot plots, & histograms

   5. Be able to produce stem-and-leaf plots, box-and-whisker plots, dot plots, & histograms from a list of data

   6. Be able to calculate percentiles given data values or data values given percentiles from stem-and-leaf plots, box-and-whisker plots, dot plots, & histograms

   7. Describe data by identifying/calculating the shape (unimodal, bimodal, uniform, right/left skew, symmetric), center (mean, median), spread (range, IQR, standard deviation), and oddities (gaps, clusters, outliers).

   8. Determine whether or not a piece of data is an outlier via both methods:

      1. Method 1:

      2. Method 2:

   9. Given the mean, standard deviation, a z-table, and a data value in an approximately normal context, be able to calculate the percentage of data above/below one piece of data, or between two pieces of data.

   10. Given the mean, standard deviation, a z-table, and a percentile in an approximately normal context, be able to calculate the corresponding data value.

2. Unit 3:One-variable data

   1. For a discrete random variable that does not follow any particular distribution:

      1. Construct a probability table of a random variable described in a paragraph.

      2. Read a probability table to answer questions about the random variable.

      3. Use the expected value to inform decisions in the context of the situation.

   2. For random variables that follow a particular distribution (binomial, geometric, Poisson, exponential):

      1. Be able to distinguish and identify when a distribution is…

         1. Binomial: if X is a number of successes in a set number of trials,

         2. Geometric: if X is the number of trials it takes to achieve the first success.

         3. Poisson: if X is the number of successes in a set window of time/space.

         4. Exponential: if X is the amount of time/space elapsed between two successes.

      2. For binomial probabilities, identify what is n (number of trials) and p (probability of a success).

      3. For geometric probabilities, identify what is p (probability of a success).

      4. For Poisson probabilities, identify what is , the rate of successes (usually )

      5. For exponential probabilities, identify what is , the rate of successes (usually )

      6. For binomial distributions, annotate what each part of the equation accomplishes or represents.

      7. For geometric distributions, annotate what each part of the equation accomplishes or represents.

   3. For all probability distributions (general, binomial, geometric, Poisson, exponential):

      1. Use correct probability notation when calculating probabilities.

      2. Calculate probabilities that X is equal to, more than, less than, at least, or at most a certain value.

      3. Use the technique of , when appropriate, to calculate a probability that would 1 − 𝑜𝑡ℎ𝑒𝑟 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 otherwise be too long (or infinite) to calculate. 

      4. Calculate the expected value of the random variable given a formula

      5. Interpret the expected value in context as the long term average of X over many random trials

      6. Calculate the standard deviation of the random variable given a formula

      7. Interpret the standard deviation as a typical distance from the mean that most values will be within

3. Unit 4:Collecting data and conducting studies (There will not be any questions on coding. There will be 3 MCQs on Law of Large Numbers / Simulation.)

   1. Interpret and apply the Law of Large Numbers, which is the principle that as trials/sample size increase, the results of the data tend towards the true values.

   2. Know what simulations can and cannot do (can save resources, predict frequency of different outcomes, consider different criteria; cannot predict what the outcome will be on any single trial).