Know the “anatomy” of data (i.e., observations and variables, quantitative and categorical variables).
Be able to identify the different types of quantitative and qualitative variables.
Understand samples versus populations.
Understand statistics versus parameters.
Understand descriptive versus inferential statistics.
What is meant by a distribution?
Be able to construct a frequency table from a small set of observations and know to find the frequency, relative frequency, and cumulative relative frequency
Know how to construct a dot plot, stem plot, and a histogram given a small set of observations.
Be able to compute a mean, median, and mode given a small set of observations. Note that you should also know how to compute a mean using a frequency table.
Know how to compute a proportion
Know how to find the modal category of a qualitative variable
Be able to compute and interpret the variance and standard deviation given a small set of observations
Know how to compute the five-number summary of a variable.
Understand how plot a cumulative distribution and use it to find the percentiles or quartiles of a distribution.
Know how a box plot is constructed from a five number summary.
Know how to interpret the shape (symmetry, skew, modality) of a distribution and how it is related to the mean and median
Know how to use the \(1.5\times IQR\) Rule to identify outliers.
Understand what it means to say that a summary measure is resistant to outliers, and which summary measures we have discussed that are resistant and which are not
Be sure you understand the notation (i.e., symbols) we have used so far (e.g., \(n,N,s,s^2,\bar{x}, \mu,\sigma,\sigma^2\)
The following formulas will be provided on the the exam \[\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i, \ \ \bar{x} = \frac{1}{n}\sum_{x} xF(x), \ \ \bar{x} = \sum_{x} xRF(X)\]
\[s^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2, \ \ s = \sqrt{\frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2}\]
\[ \text{range}(x) = \text{min}(x) - \text{max}(x), \ \ IQR = Q3 - Q1 \]
\[x < Q1 - 1.5 \times (Q3 - Q1), \ \ x > Q3 - 1.5\times(Q3-Q1)\]