To determine whether it is appropriate to make a pie chart of the data given in the frequency table, we need to consider a few key points about pie charts.
A pie chart is a circular chart divided into slices to illustrate numerical proportions or percentages of a whole. For a pie chart to be appropriate:
- The data should represent parts of a whole.
- The total of all the parts (slices) should sum to 100%.
Given the frequency table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Age Category} & \text{Percentage} \\
\hline
$13-18$ & $29\%$ \\
\hline
$19-29$ & $23\%$ \\
\hline
$30-49$ & $19\%$ \\
\hline
$50-64$ & $10\%$ \\
\hline
65 \text{ and older} & $4\%$ \\
\hline
\end{tabular}
\][/tex]
Let's analyze the criteria:
1. Are the data expressed as percentages?
- Yes, the data in the table are shown as percentages (29%, 23%, 19%, 10%, 4%).
2. Are the data grouped into categories?
- Yes, the data are grouped into age categories.
However, looking closer:
3. Do the data represent parts of a whole?
- No, the percentages represent the portion of free time spent on smartphones within each age category, not a relative distribution of these groups as parts of a whole. They are individual percentages rather than a part of a single sum.
4. Do the data categories sum to 100%?
- No, the sum of the percentages ([tex]$29\% + 23\% + 19\% + 10\% + 4\% = 85\%$[/tex]) does not total 100%. Even more crucially, these percentages do not reflect parts of a singular whole, but are rather isolated metrics within distinct age groups.
Given these points, a pie chart is not appropriate for these data because the values represent the percentage of time an individual within each age category spends on their smartphone, not how the age categories themselves are proportionally distributed in terms of their smartphone use. This misrepresentation would be misleading if depicted as parts of a whole.
Hence, the correct answer is:
- No, the data represent the percentage of time spent by each individual, not a relative frequency compared to the whole.
