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When we talk about a measure of central tendency, we refer to a single value that represents the center point or typical value of a dataset. It aims to provide an accurate description of the entire data set with just one number. The three main measures of central tendency are the mean (average), median, and mode.

The mean is calculated by adding up all the numbers and then dividing by the count of numbers. However, the mean can be heavily influenced by outliers, which are values significantly higher or lower than the rest. In a balanced dataset, the mean is an excellent measure as it incorporates every value.

The median is the middle value when you order the data from least to greatest, and it is not affected by outliers. This makes it particularly useful in skewed distributions. It provides a more accurate 'typical' value in such cases.

The mode is the most frequently occurring value in the dataset. It can be useful in datasets with a high frequency of a particular value.

The difference between the average (mean) and median can be significant, especially if the data is skewed. Average is calculated by summing all the numbers in a data set and dividing by the count of numbers, which can result in an unrepresentative measure if there are extreme numbers in the set (i.e., outliers). For instance, in a neighborhood with mostly modest houses but a couple of mansions, the average home price will be much higher because of the mansions' influence, but that average wouldn't reflect what most people pay for a house.

The median, being the middle value, effectively cuts the dataset in half, ensuring that half the values are below it and half above. This makes the median a better measure when there's a skewed distribution, as it is less affected by extremely high or low values. It more accurately reflects the 'typical' value that most data points are closer to.

For the given exercise data, with such a broad spread in circulation numbers and a clear gap between the leading figures and the majority, median provides a more accurate representation of a typical news magazine's circulation.

A skewed distribution occurs when the data points cluster more on one side of the scale than the other, creating a long tail in the opposite direction of the cluster. If the tail is to the right, it's called a positive skew, and if it's to the left, it's a negative skew.

In a positively skewed distribution, the mean will be greater than the median, because the few high values pull the mean upwards. Conversely, in a negatively skewed distribution, the mean will be less than the median, influenced downward by the low values. Therefore, analysts prefer the median in skewed distributions because it's a better representation of where the middle of the data truly lies.

Returning to our exercise data, the presence of a single very high circulation number creates a positively skewed distribution. Using the mean here gives a false impression that the typical magazine has a higher circulation than what's true for most of the data set. That is why, for such data, other central tendency measures like median or mode are usually preferred.