Questions: Determine the original set of data. Stem Leaves 5 7 6 2 7 09 8 5 9 37 10 69 11 679 12 2389 13 79 Legend: 517 represents 5.7

Transcript text: Determine the original set of data. \begin{tabular}{|c|c|} \hline Stem & Leaves \\ \hline 5 & 7 \\ \hline 6 & 2 \\ \hline 7 & 09 \\ \hline 8 & 5 \\ \hline 9 & 37 \\ \hline 10 & 69 \\ \hline 11 & 679 \\ \hline 12 & 2389 \\ \hline 13 & 79 \\ \hline \end{tabular} Legend: 517 represents 5.7

Solution

Solution Steps

To determine the original set of data from the given stem-and-leaf plot, we need to combine each stem with its corresponding leaves. Each leaf represents a digit that follows the stem, and the legend indicates that the numbers are in the format of one decimal place.

Step 1: Extracting Data from the Stem-and-Leaf Plot

We start by extracting the data from the given stem-and-leaf plot. Each stem represents the integer part of the number, and each leaf represents the decimal part. According to the legend, the number \(517\) represents \(5.7\).

Step 2: Combining Stems and Leaves

We combine each stem with its corresponding leaves to form the original data set. For example, the stem \(5\) with leaf \(7\) forms the number \(5.7\).

Step 3: Listing the Original Data

The original data set is obtained by combining all stems and leaves as follows: \[ \begin{align_} 5 & : 7 \rightarrow 5.7 \\ 6 & : 2 \rightarrow 6.2 \\ 7 & : 0, 9 \rightarrow 7.0, 7.9 \\ 8 & : 5 \rightarrow 8.5 \\ 9 & : 3, 7 \rightarrow 9.3, 9.7 \\ 10 & : 6, 9 \rightarrow 10.6, 10.9 \\ 11 & : 6, 7, 9 \rightarrow 11.6, 11.7, 11.9 \\ 12 & : 2, 3, 8, 9 \rightarrow 12.2, 12.3, 12.8, 12.9 \\ 13 & : 7, 9 \rightarrow 13.7, 13.9 \\ \end{align_} \]