The following table shows the ages of competitors in a...

The following table shows the ages of competitors in a charity tennis event in Rome: $$ \begin{array}{cc} \hline \text { Age } & \text { Percent } \\ \hline 18-24 & 18.26 \\ 25-34 & 16.25 \\ 35-44 & 25.88 \\ 45-54 & 19.26 \\ 55+ & 20.35 \\ \hline \end{array} $$ a. Construct a relative cumulative frequency distribution. b. What percent of competitors were under the age of 35 ? c. What percent of competitors were 45 or older?

The following table shows the ages of competitors in a charity tennis event in Rome:

$$
\begin{array}{cc}
\hline \text { Age } & \text { Percent } \\
\hline 18-24 & 18.26 \\
25-34 & 16.25 \\
35-44 & 25.88 \\
45-54 & 19.26 \\
55+ & 20.35 \\
\hline
\end{array}
$$
a. Construct a relative cumulative frequency distribution.
b. What percent of competitors were under the age of 35 ?
c. What percent of competitors were 45 or older?

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Key Concepts

Relative Frequency Distribution

A relative frequency distribution displays the proportions or percentages of the total number of observations that fall within each category. Instead of listing raw counts, it shows each category’s frequency relative to the total count, often expressed as a decimal or percentage. This format helps in understanding the distribution of data in relation to the whole data set.

Cumulative Frequency Distribution

A cumulative frequency distribution is a running total of frequencies through the classes in an ordered data set. Each value in a cumulative frequency table represents the sum of the frequencies for that category and all previous categories. When expressed in relative terms, it shows the proportion or percentage of data below the upper boundary of each class, and is useful for identifying the median, percentiles, and overall data spread.

Percentage Calculation for Grouped Data

In the context of grouped data, calculating percentages involves summing the individual percentages of data groups to determine the proportion that meets a certain criterion. This approach is essential when dealing with summed intervals or ranges, such as determining the proportion of observations that fall below or above a specific threshold.

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