Practice by changing different aspects of a problem, such as a numerical value, and predicting what will happen to the solution.  Then be able to explain, intuitively and mathematically, why the prediction you made is reasonable.

For instance, if you add a value to a data set and this value is larger than any previous value in the data, what happens to the measures of central location (mean, median, and mode)?  Intuitively, the center of the data set should shift upward when larger values are included in the data set.  This argument works well for the mean, less well for the median, and least well for the mode.  The order of these measures reflects the respective sensitivity of each to the addition of a single new value to a data set.  We see this in the mathematical explanation.  Every value in a data set is included in its computation.  Computation of the median comes from one or two values in the middle.  Changing values at the bottom or top will not affect the value of the median.  Adding such values will not shift the median in the opposite direction (adding a large value will not make the median smaller).  It may stay the same or shift in the direction of the new value.  The mode reflects the value that occurs most often in the data set.  A new large value could change the mode if there are a lot of the same values, but this is likely to be an unusual occurrence for most data sets.

Another example, if I ask you what will happen to the width of a confidence interval if you increase the confidence level (decrease the risk level), you should know that the width increases.  Mathematically, the z values increase when we increase the confidence3 level.  Thus, the amount that you add and subtract from the estimate increases, and a wider confidence interval results.  Intuitively, when we increase the confidence level, we mean that we want to be more confident the interval contains the true population value.  The only was to do this, when we don't change anything else in the problem, is to widen the confidence interval so that it contains more potential values for the population value.

Many of the worksheets offer practice in this type of exercise, and you can invent some of your own.  You can check these out with me.
 

 Return to Prevention Menu
 Return to Stat Trailhead
 Return to Trailheads