Question

State whether a cumulative frequency, relative frequency, relative percent, cumulative relative frequency, or cumulative percent is most appropriate for describing the following situations. For cumulative distributions, indicate whether these should be summarized from the top down or from bottom up.

a. The proportion of Americans earning $30,000 at most.

Answer 1

For the proportion of Americans earning $30,000 or less, a cumulative relative frequency from the bottom up is suitable, combining relative frequencies up to that income level to show the percentage of the population within this range.

Step-by-step explanation:

For describing the proportion of Americans earning $30,000 at most, a cumulative relative frequency distribution is most appropriate. This statistic will provide the sum of the individual relative frequencies of all income categories up to and including the $30,000 category, which shows how much of the population falls within this income range. Typically, cumulative distributions are summarized from the bottom up, meaning that we start from the lowest value (in this case, the lowest income) and add the frequencies of each subsequent category to the previous total to provide a running total that culminates in 100%.

A relative frequency shows the fraction or proportion of the number of times a value occurs relative to the total number of outcomes. When you want to find out how many individuals in a certain group earn $30,000 or less, you would calculate the relative frequencies for the earnings categories and then sum them to find the cumulative relative frequency. When this cumulative value reaches the $30,000 level, we can say, for instance, that 'x' percent of the studied population earns $30,000 or less.