Question

why may only one measure of central tendency be an inadequate description of a data set?

Answer 1

WE know that the arithmetic mean is based on all observations in the data set. If the data set consists of outliers, then the arithmetic mean does not work properly as a measure of central tendency. In this case, we need to use median or mode depends on the nature of the data set. We know that the median and mode are not affected due to the extreme values of the data set. Sometimes, we need to use mode as a measure of central tendency when most of the data concentrated around the particular value. Also, we need to use geometric mean or harmonic mean as a measure of central tendency if the data is related to the time, interest, etc. So, for getting information about the data set, it is important to use more than one measure of central tendency. Use of only one measure of central tendency is not adequate, because we do not get exact idea about the data set. For example, if we know the values for mean, mode, and median, and all these are approximately equal, then we can say that given data is approximately symmetric.