Question

Sharing music online (5.2, 5.3). A sample survey reports that 29% of Internet users download music files online, 21% share music files from their computers, and 12% both download and share music. Make a two-way table that displays this information.

Two-way tables
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asked 2020-10-27
Sharing music online (5.2, 5.3). A sample survey reports that 29% of Internet users download music files online, 21% share music files from their computers, and 12% both download and share music. Make a two-way table that displays this information.

Answers (1)

2020-10-28
We are interested in the proportion of Internet users that download music files online and that share music files from their computers.
Let us name the columns of the two-way table "download online” and "do not download online”, while we name the rows of the two-way table "share music files” and "do not share music files”.
\(\begin{array} {c|cc|c} & \text { Download online } & \text { Do not download online } & \text { Total } \\ \hline \text { Share music files } & & &\\ \text { Do not share music files } & & & \\ \hline \text { Total }& &\end{array}\)
29% of the Internet users download music files online, while 21% share music. files and 12% do both. We also know that the table needs to contain 100% of the Internet users in total.
The remaining percentages can be determined using the known row/column totals.
\(\begin{array} {c|cc|c} & \text { Download online } & \text { Do not download online } & \text { Total } \\ \hline \text { Share music files } & 12\% & 21\%-12\%=9\% & 21\% \\ \text { Do not share music files } & 29\%-12\%=17\% & 71\%-9\%=62\% & 100\%-21\%=79\% \\ \hline \text { Total } & 29\% & 100\%-29\%=71\% & 100\% \end{array}\)
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\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)
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