Final answer:
Measures of central tendency, such as the mean, can be misleading in data sets with outliers. For example, an extremely high income in a set of salaries can skew the mean upwards, not reflecting the typical income accurately. To avoid such misrepresentations, the median or visual data representations are preferable.
Step-by-step explanation:
An example that demonstrates why measures of central tendency can be misleading involves a scenario where the data set contains extreme values or outliers. Suppose we are looking at the incomes of a group of people in a region. If we have a data set consisting of incomes of $30,000, $35,000, $40,000, and one outlier of $1,000,000, the mean income would be significantly skewed by the outlier, suggesting an average income much higher than most people in the group actually earn. On the other hand, the median, which is the middle value when the data set is ordered, would give a more accurate representation of what a 'typical' income in this region looks like.
To mitigate misleading conclusions, one might also consider using additional statistics such as the mode, which is the most frequently occurring value, or visual displays like histograms or box plots that can provide a more comprehensive understanding of the data distribution. This will help in recognizing the skewness and the effects of outliers on the given data set.