In a relative frequency distribution, what is the sum of all the relative frequencies?

In a relative frequency distribution, what is the sum of all the relative frequencies?

• A. 1
• B. The total number of observations
• C. The maximum relative frequency
• D. The mean

Answer: (A)

In a relative frequency distribution, each category’s relative frequency is its share of the total observations. All those shares must add up to the whole, so their sum is 1 (or 100% if expressed as percentages). You can see this mathematically: if you call the category frequencies f_i and the total N, then sum over all categories of f_i/N equals (sum f_i)/N, which is N/N, or 1. This reflects that relative frequencies are proportions that describe the whole dataset. The total number of observations is N, not a proportion. The maximum relative frequency is just the largest category’s share, not the total. The mean is a measure of central tendency, not the sum of part proportions. Therefore, the sum of all relative frequencies is 1.

In a relative frequency distribution, each category’s relative frequency is its share of the total observations. All those shares must add up to the whole, so their sum is 1 (or 100% if expressed as percentages). You can see this mathematically: if you call the category frequencies f_i and the total N, then sum over all categories of f_i/N equals (sum f_i)/N, which is N/N, or 1. This reflects that relative frequencies are proportions that describe the whole dataset. The total number of observations is N, not a proportion. The maximum relative frequency is just the largest category’s share, not the total. The mean is a measure of central tendency, not the sum of part proportions. Therefore, the sum of all relative frequencies is 1.