What is the mode, median, and mean?What levels of measurement are they most useful for

Question

What will be an ideal response?

Answer 1

The mode is one measure of central tendency. The mode conceptualizes “central tendency” in terms of what is the most likely, most common, or most frequent score in a distribution of scores. Another way to think of the mode is to note that it is the score or value that has the highest probability of occurring. The mode can be calculated with data measured at the nominal, ordinal, or interval/ratio level. However, if you have nominal- or purely ordinal-level data (purely ordinal in the sense that the data are not continuous data that you have made ordinal by making class intervals or grouping your data), then the mode is the only appropriate measure of central tendency that you may legitimately use.
The median is an appropriate measure of central tendency for quantitative data measured at the interval/ratio level or for data that may have originally been measured at the interval/ratio level but now consist of grouped data (class intervals for grouped frequency distributions that have real limits). The easiest way to think of the median is that it is the value that is at the 50th percentile in a rank-ordered distribution of scores. The median score, in other words, is the score in the exact middle of a rank-ordered distribution of quantitative scores such that the median is the point above which one-half of the scores are and below which the other one-half of the scores fall.
The mean is defined as the arithmetic average of a group of scores and is calculated by summing all of the scores and then dividing by the total number of scores. The mean requires that the data be measured at the interval/ratio level.