One strength of using the mode is that it is easy to calculate and less prone to distortion by freak values as it does not take into account all the data unlike the mean which is highly influenced by freak scores as it takes all data into account.
One disadvantage of using the mode is that it does not take account of all scores so it may be less accurate unlike the mean which takes all data into account. Moreover, the mode may not be useful if there is more than one mode in a data set.
One strength of using the median is that it is easy to calculate and less prone to distortion by freak values as it does not take into account all the data unlike the mean which is highly influenced by freak scores as it takes all data into account.
One disadvantage of using the mean is that it is not as sensitive as the mean as it does not use all scores meaning the results may be less useful.
One strength of using the mean is that it is the most accurate and sensitive measure of central tendency as it uses all data sets unlike the median/mode which does not take into account all of the data.
One disadvantage of using the mean is that it is affected by freak scores as it takes all scores into account which can result in misleading interpretation of results.