Answer :
To get to the answer for why one graph appears skewed and one appears symmetrical, let's examine each possible explanation given the data provided in the stem-and-leaf plot:
[tex]\[ \begin{tabular}{|c|c|} \hline 1 & 0145 \\ \hline 2 & 33566 \\ \hline 3 & 1668999 \\ \hline 4 & 012246 \\ \hline 6 & 0236 \\ \hline 7 & 01 \\ \hline \end{tabular} \][/tex]
1. The scale of the box-and-whisker plot does not start at zero.
- If the scale of a box-and-whisker plot does not start at zero, it might truncate some values, but this would not inherently cause one graph to look skewed versus symmetrical. Therefore, this explanation is unlikely.
2. The interval of the box-and-whisker plot is too large.
- If the interval of the box-and-whisker plot is too large, it could affect the detail seen in the data, but it generally wouldn't cause asymmetry directly. So, this explanation is not the most fitting either.
3. The interval of the stem-and-leaf plot is not consistent.
- If the intervals in the stem-and-leaf plot are inconsistent, it would distort the data representation causing one graph to appear skewed. Reviewing the intervals in the provided stem-and-leaf plot, it seems indeed possible there is inconsistency, making this explanation very plausible.
4. The scale of the stem-and-leaf plot is too small for the set of data.
- If the scale of the stem-and-leaf plot is too small, it means it may not accommodate all data values accurately, potentially causing distortion. However, the problem described is about inconsistency rather than insufficient scale.
Given these considerations, the best explanation for why one graph appears skewed and one appears symmetrical is:
The interval of the stem-and-leaf plot is not consistent.
Hence, the correct answer is:
The interval of the stem-and-leaf plot is not consistent.
[tex]\[ \begin{tabular}{|c|c|} \hline 1 & 0145 \\ \hline 2 & 33566 \\ \hline 3 & 1668999 \\ \hline 4 & 012246 \\ \hline 6 & 0236 \\ \hline 7 & 01 \\ \hline \end{tabular} \][/tex]
1. The scale of the box-and-whisker plot does not start at zero.
- If the scale of a box-and-whisker plot does not start at zero, it might truncate some values, but this would not inherently cause one graph to look skewed versus symmetrical. Therefore, this explanation is unlikely.
2. The interval of the box-and-whisker plot is too large.
- If the interval of the box-and-whisker plot is too large, it could affect the detail seen in the data, but it generally wouldn't cause asymmetry directly. So, this explanation is not the most fitting either.
3. The interval of the stem-and-leaf plot is not consistent.
- If the intervals in the stem-and-leaf plot are inconsistent, it would distort the data representation causing one graph to appear skewed. Reviewing the intervals in the provided stem-and-leaf plot, it seems indeed possible there is inconsistency, making this explanation very plausible.
4. The scale of the stem-and-leaf plot is too small for the set of data.
- If the scale of the stem-and-leaf plot is too small, it means it may not accommodate all data values accurately, potentially causing distortion. However, the problem described is about inconsistency rather than insufficient scale.
Given these considerations, the best explanation for why one graph appears skewed and one appears symmetrical is:
The interval of the stem-and-leaf plot is not consistent.
Hence, the correct answer is:
The interval of the stem-and-leaf plot is not consistent.
