When there is one missing value in a data set, what method should be used to estimate that value?

The median is the most appropriate method for estimating a missing value in a data set, particularly when the data may contain outliers or is skewed. The median represents the middle value when the data is arranged in ascending order, making it a measure of central tendency that is less affected by extreme values compared to the mean. This robustness allows for a more accurate reflection of the dataset's typical value when some data points are absent.

In contrast, the mean can be influenced by high or low values, leading to potentially misleading estimates when trying to fill in a missing value. The mode, which identifies the most frequently occurring value in the data set, might not provide a representative estimate for a missing value, especially in cases of continuous data or when multiple modes exist. The range simply reflects the difference between the highest and lowest values in the dataset, providing no insight into the central tendency needed to estimate the missing value. Therefore, using the median offers a balanced approach that maintains the integrity of the data distribution when one value is missing.