In statistics, picking the median instead of the mean can be very important in certain situations.

• Outliers: Sometimes, a data set has extreme values called outliers. These can really change the mean. For instance, if we look at income data, a few people making a lot of money can push the mean up, making it not truly reflect what most people earn. The median, which is the middle value, isn't affected by these high or low numbers. This makes it a better way to see the average situation.

• Skewed Distributions: If the data isn’t evenly spread out, like in right-skewed distributions (where there are more low values and a few really high ones), the mean can give a higher number than what most values actually show. The median gives a clearer picture of where most of the data points are situated.

• Ordinal Data: Sometimes, the data we use is ordinal, which means it’s ranked in order. Using the mean can make things confusing in this case. The median is much better at summarizing these kinds of data and is the preferred option.

• Uneven Group Sizes: When comparing groups that are not the same size, the mean might be unfair and favor the larger group. The median helps balance the comparison across different populations.

In summary, the median works better when the data has certain features, like outliers or is not evenly distributed. Using the median ensures that we clearly understand the average of the data.