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Understanding what an outlier is can be crucial when interpreting data. Simply put, an outlier is a value that is significantly different from most of the data in a set. Imagine you're looking at the heights of a group of people, and most are between 5 to 6 feet tall. If one person measures 8 feet, that value is an outlier because it's abnormally far from the others.

Outliers can occur naturally in a dataset due to the diversity or variability of data. However, sometimes they indicate a measurement or recording error, or they could suggest that the data comes from a different population. Detecting outliers is essential because they can skew our analysis, leading to inaccurate conclusions.

When you come across an outlier, the first step is to consider why it might be there. If an error caused it, correcting or removing the error is usually best. But if the outlier reflects genuine variation, you have several options. You could annotate it as notable, analyze it separately from the rest of the data, or adjust your statistics to reduce its impact, using techniques like log transformation.

Moreover, if you decide that the outlier doesn't represent your data well, you could treat it as missing data. This means you wouldn't use it for calculations like averages, which could otherwise be distorted by the atypical value.

When analyzing data, choosing a central tendency measure that is robust to outliers helps provide an accurate picture. The median, the middle point in a dataset when values are ordered from smallest to largest, is noted for being resistant to outliers. Adding an extreme value doesn't shift the median much, as it depends on the order of values, not their magnitude.

The median is often preferred in reports of average housing prices or incomes because these datasets can have extreme outliers that would make the mean, or average, less representative of the typical experience.

Outliers in a dataset can have a significantly different impact on the mean and the median. As the arithmetic average, the mean includes every value in its calculation. This means an extremely high or low outlier can pull the mean in its direction, potentially misrepresenting the data's center.

The median, however, isn't so easily swayed. Since it's the value at the midpoint of the dataset, it remains stable even when outliers are present. This stability is particularly useful in understanding the center when outliers represent rare or exceptional cases that don't typify the overall dataset.