Summarizing Data and Estimating Population Parameters Using Descriptive Measures

Overview and learning goals

As we embark on this topic, ask yourself: Do I understand the following concepts and disciplines and how they fit together?

  • Do I know what is a descriptive measure?
  • Can I name and distinguish between the four categories of descriptive measure, and the kinds we’re going to see of each?
  • Can I calculate and interpret the following measures of central tendency?
    • Population and sample mean
    • Median
    • Midrange
    • Mode
  • Can I calculate and interpret the following measures of variation (or variability or spread or dispersion):
    • Population and sample variance
    • Population and sample standard deviation
    • Range
    • Coefficient of variation
  • Can I calculate and interpret the following measures of position:
    • Percentiles
    • Quartiles
    • z-scores
  • Can I calculate and interpret the following measures of shape:
    • Skewness
    • Kurtosis

The learning goals above are critical and covered in most courses in statistics. Because it’s so important yet often confused or misunderstood, we’re also going to make sure you:

  • Can explain how well some of the key descriptive measures calculated from samples (i.e. sample statistics) represent the corresponding actual and most often unknown population parameters, i.e. how precise our descriptive measures are
  • Can calculate and interpret estimates of that precision using equations of the Standard Error

My notes

Here are my lecture notes – the ones I wrote up when I lectured on this topic. They’re not perfect, but if you’re in my class then they should be helpful when you go to create your own “perfect” set of lecture notes.

When you’re ready, proceed by working your way through the self-assessments (under “Lesson Assessments”) below.

Once you’ve clicked through those, use the green button to move on to the next lesson (or to finish up if there are no other lessons).

The following schedules are for Alex’s in-class students:

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