To analyze why one graph appears skewed and the other appears symmetrical, let's interpret the given stem-and-leaf plot and the provided options.
Given the leaf plot:
\begin{tabular}{|c|c|}
\hline & 0145 \\
\hline & 33566 \\
\hline & 1668999 \\
\hline & 01246 \\
\hline & 0236 \\
\hline & 01 \\
\hline
\end{tabular}
To determine the reason for the apparent skewness or symmetry, we should consider each option carefully:
1. The scale of the box-and-whisker plot does not start at zero.
- This option suggests that the problem lies with the box-and-whisker plot having a non-zero starting point, which could cause misconceptions about the distribution of the data. However, this is not the primary issue in our scenario.
2. The interval of the box-and-whisker plot is too large.
- If the intervals are too large in the box-and-whisker plot, it might cause an improper representation, but again, it’s not suggested by our stem-and-leaf plot.
3. The interval of the stem-and-leaf plot is not consistent.
- This means that the spacing between intervals is variable and not uniform. Let’s examine our plot:
- Stem 0: 0, 1, 4, 5
- Stem 3: 3, 3, 5, 6, 6
- Stem 1: 1, 6, 6, 8, 9, 9, 9
- Stem 0: 0, 1, 2, 4, 6
- Stem 0: 0, 2, 3, 6
- Stem 0: 0, 1
Here, stems are repeated which suggests inconsistency. This means that one part might represent a certain interval while another part represents a different length, leading to a misrepresentation of data. This makes this option the most plausible explanation for the skewness observed.
4. The scale of the stem-and-leaf plot is too small for the set of data.
- If the scale is too small, the data representation gets compressed, making it hard to visualize the distribution accurately. However, the main issue with the given plot is not compression but inconsistency, as indicated earlier.
Therefore, after carefully analyzing the data and the given options, the most appropriate explanation is:
The interval of the stem-and-leaf plot is not consistent.
