Tabular Representation and Summary Statistics for One Categorical Variable

For one categorical variable, a frequency table counts the observational units in each category, and the counts sum to the total number of units. Dividing each count by that total gives the relative frequency table: the proportion of units in each category, summing to 1. Percentages, proportions, and ratios are the same information in different dress. Counts answer how many; relative frequencies answer how common; and only the relative frequencies compare fairly across groups of different sizes, because dividing by each group's own total puts every group on the same scale.

The reliable failure here is comparing raw counts across unequal groups and crowning the bigger count the stronger tendency - 300 walkers at a school of 2,000 beating 150 at a school of 500, when the shares run 15% against 30% the other way. Its quieter siblings: reading a relative frequency as a headcount, splitting the total evenly across categories as if shares came free, and letting percentages total more than 100 for a choose-one question. A separate miss is treating the categories themselves as numbers and averaging them, which belongs to the previous topic and still shows up in this one.