John said Mary could know about the error is she calculated the standard error of the mean and the coefficient of variation.

Yes, calculating the standard error of the mean and the coefficient of variation can help Mary to know about the error. The standard error of the mean is a measure of the variability of a sample mean, and the coefficient of variation is a measure of the relative variability of a sample. By calculating these two values, Mary can get an idea of the amount of error in her data.