In a nutshell: There is some confusion and new information surrounding which probability and statistics concepts we cover and which ones we don’t. We’ve created a list to help you out!
We have mentioned before that the upper limit of the probability and statistics material that we cover is defined by the High School Statistics and Probability section of the Common Core State Standards for math.
However, the language in some of these standards is not very exact. For example, one particular standard claims that students have to be able to use the mean and standard deviation for a normally distributed data set to estimate population percentages. This implies (without explicitly stating) that they need to calculate and use z-scores.
To display our updated policy and clear up the confusion once and for all, here is a comprehensive outline of the concepts in probability and statistics that we expect Yup Math Tutors to be able to cover by the start of the upcoming school year (topics not originally included by the Tutor Policies document are in green text):
- Basic probability (e.g. if there are 3 blue blocks and 4 green blocks in a bag, what is the probability of a randomly chosen block turning out to be blue?)
- Compound events
- Choosing objects with and without replacement
- Mutual exclusivity
- Dependent vs. independent events
- Addition and Multiplication Rules
- Conditional probability (Bayes’ theorem)
- Permutations and combinations
- Calculating expected values (e.g. It costs $5 to play a gambling game that has a 1% chance of paying you $200 and a 10% chance of paying you $20. What is the expected payout of the game?)
- Central tendency in data sets (mean, median, mode)
- Spread in data sets (standard deviation, interquartile range, outliers)
- Understanding when a probability distribution is normal, skewed right, or skewed left (68-95-99.7 rule)
- Using mean and standard deviation of a normally distributed data set to estimate population percentages (e.g. calculating z-scores)
- Using sample means and standard deviations to test for statistical significance (specifically: null and alternate hypotheses, one- and two-tailed t-test, p-values, chi-squared goodness of fit test, and degrees of freedom)
- Finding the population proportion and margin of error for a given population parameter and confidence interval
- Understanding scatter plots, box-and-whisker plots, stem-and-leaf plots, and histograms
- Frequency (relative, joint, marginal, and conditional) in two-way data tables
- Basic sampling methods and biases
- Simple random sampling
- Different between sample survey, experiment, observational study
- Basic principles of lines of best fit (regression lines)
- Fitting regression lines
- Finding the correlation coefficient (using a calculator)
- Understanding that correlation does not imply causation
- Interpreting the slope and y-intercept for a data set
- Plotting residuals
We still do not cover certain advanced probability distributions (e.g. Poisson or geometric), advanced hypothesis tests (e.g. ANOVA), Type I and II errors, or any other concepts that are not found in the Common Core. Since we realize that much of this material has not been mentioned in the past, here are a few resources (among many) that you can use to update/refresh your knowledge on any of the material mentioned above.
In addition, there will be a 3-week period, starting today, in which you will not be given an infraction for telling students you cannot solve a problem if it contains statistics concepts that we previously regarded as outside our coverage. Use it wisely!!
–Team Yup
The engineering team will incorporate the new tags into your Tutor Dashboard on the night of Friday, August 26th. (FYI: the Session Categorization document, linked to in slide 7, still refers to the old tagging system.)
