What summary statistics are affected by adding a constant to each data value?

When a constant is added to each data value in a dataset, the mean and median will be directly affected. This occurs because both the mean and median are measures of central tendency that depend on the actual values in the dataset.

The mean is calculated by summing all the values and dividing by the count of values. When a constant is added to each data point, the total sum increases by the number of data points multiplied by that constant. As a result, the mean shifts upward by the same constant.

Similarly, the median, which represents the middle value when the data is ordered, shifts as well. Adding a constant to each value does not change the order of the values but merely shifts all of them by the same amount. Therefore, the median increases by that constant as well.

Other summary statistics, such as the mode, variance, and standard deviation, do not respond in the same way. The mode, which identifies the most frequently occurring value, remains unchanged regardless of the constant added, unless the constant coincides with an existing mode. Variance and standard deviation are measures of dispersion and are calculated based on the distances between the data points. Adding a constant does not affect these distances; hence, they remain unchanged.

Thus, the correct answer