Math 207 – Important Additions to Chapters 1 and 2

· Throughout the course we will talk about the distribution of a variable or an estimator. The distribution is defined as what values a variable takes on and how often. In any graphical display of a distribution, look for the overall pattern and for striking deviations from that pattern. The overall pattern of a distribution can be described by its shape, center, and spread (i.e., variability).

· The textbook only discusses the range and the standard deviation in its section on “measures of variability.” The interquartile range (mentioned later in Chapter 2) is also a measure of variability. (Also note that the standard deviation is affected by extreme values, whereas the interquartile range is not.)

· The mean is affected by outliers, while the median is not. Hence, for skewed distributions, the median is a better measure of typical value. Now recall the standard deviation measures the spread of a distribution around its mean. So if the mean is not a good measure of center (e.g., for a skewed distribution), then the standard deviation shouldn’t be used as a measure of spread. Therefore, for skewed distributions, the five-number summary is a more appropriate and informative summary than simply reporting the mean and standard deviation (for a symmetric, mound-shaped distribution, the mean and standard deviation provide all the necessary information).

The next two bullet points address the importance of writing well about statistics

· Always put your analysis in context. That is, include information on the individuals being measured, the variable being measured, and the units of measurement. After you have written your analysis, ask yourself whether a stranger could read your words and completely understand the topic and the context.

Here is an example progression from poor statistical writing to strong statistical writing:

The median is 75.

The median is 75 beats per minute.

The median resting heart rate is 75 beats per minute.

The median resting heart rate of patients is 75 beats per minute.

The median resting heart rate of recent patients at the Makemewell Clinic is 75 beats per minute.

· In a similar vein, be specific (rather than general) in your descriptions, linking them to the setting of the problem.

Here is an example progression from general (and non-informative) statistical writing to specific statistical writing:

The data are skewed.

The data are skewed right.

The distribution of resting heart rates is skewed right.

The distribution of resting heart rates of recent patients at the Makemewell Clinic is skewed right.