Below are some helpful hints and tips for tutors of Statistics 303. The change of textbooks this semester goes along with some slight adjustments to teaching philosophies, and I hope the following will be helpful to everyone.
We're emphasizing the difference between samples and populations and trying to help students understand the big idea of
statistical inference from the beginning because we believe it will help students keep from getting lost when we get
to the details of the CLT in later chapters.
We summarize categorical data with pie charts, bar charts, proportions, and frequency tables; categorical data take up
much less of our time and energy in these chapters. For quantitative data, we emphasize three important ways to describe
the distributions: shape, center, and spread. This comes from the normal distribution being more common: once we know
that a distribution is normal, and we know its mean and standard deviation, we know everything else about it; the normal
distribution has only two parameters (mu and sigma). The Poisson distribution has mean equal to variance, so we actually
only need shape and center for that particular distribution, but most of the most common distributions have two
We're emphasizing the skill of predicting the shape of the distribution of a variable in this textbook; it helps
students understand better what they're looking at when they see a normal curve. The idea that the variable is on
the x-axis and its frequency is on the y-axis is not at all intuitive to beginning students. Even Excel when making a
bar chart by default gives each observation a separate bar; the value of the variable is the height of the bar, which
isn't a histogram at all. I'm using this example in class because I want to emphasize that a main point of
calculating a statistic or drawing a graph is to take a large pile of information and summarize it into something simple
that I can understand. Excel bar charts aren't summarizing the data when they draw a separate bar for each observation.
Students often struggle with the word "average" in a statistics class. The second definition of "average" on Dictionary.com
is "a typical amount, rate, degree, etc.; norm." This is confusing because the arithmetic mean is often not typical or
normal, and the definition "arithmetic mean" is the one used in a statistics course. We work hard to emphasize that the
median is a better measurement of what is typical in the case where we have outliers or skewness.
Variability is the reason we need statistics and statistical thinking. Variability within a single sample means sampling
variability also exists; we're laying down the foundation for standard error in this chapter. We help students understand
standard deviation as a measurement of the typical distance between an observation and the mean; while the formula for
standard deviation is not strictly equivalent to an average distance for the mean, the standard deviation and the average
distance from the mean are usually similar to each other. "Typical distance from the mean" is a fine interpretation of
standard deviation for students to use.