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Median is the same for both data sets A and B.

The median, which represents the middle value in a data set when arranged in order, is the correct measure that remains constant across both data sets A and B.

A) Median

The median is the value that separates the higher half from the lower half of a data set. Since it is based on the position of values rather than their magnitude, it can be the same for different distributions as long as the middle values remain unchanged.

B) Mean

The mean, or average, is calculated by summing all values and dividing by the number of values. This measure can vary significantly between two data sets, especially if they have different ranges or distributions, making it an unreliable comparison for data sets A and B.

C) Range

The range is defined as the difference between the highest and lowest values in a data set. Since this measure depends heavily on the specific values present in each data set, it is unlikely to be the same for both data sets A and B unless they are identical in their extremities.

D) Upper quartile

The upper quartile, representing the value below which 75% of the data falls, is sensitive to the specific values within a data set. It can differ between data sets A and B depending on their distribution, and therefore, it is not a measure that would necessarily be the same for both.

Conclusion

The median stands out as the only measure that can be the same for both data sets A and B, as it is determined by the position of values rather than their actual values. In contrast, the mean, range, and upper quartile are all influenced by the specific data points and can vary significantly between different data sets. Thus, the median is the definitive answer to this question.