Why the median value is used for NaN? Why not something else like mean? What is the logic behind using the median value?

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The process you described is known as imputation. Whether it makes sense to impute missing values with mean or median depends entirely on the dataset and the context of your problem.

Usually, it does not hurt to impute missing values with the mean. However, if there are outliers in the dataset that adversely impact the mean, then it is probably a good idea to impute with the median, as the median is a metric that is not influenced by the presence of outliers in the dataset.

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