To determine if the histogram of the given data is symmetrical, we'll first construct the histogram and then interpret its symmetry properties.
Here is a detailed, step-by-step solution:
1. Data Given: We start with the list of hours:
[tex]\[
[9, 1, 8, 7, 9, 9, 8, 9, 8, 7]
\][/tex]
2. Constructing a Frequency Table:
We count the occurrences of each value in the list.
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours} & \text{Frequency} \\
\hline
1 & 1 \\
7 & 2 \\
8 & 3 \\
9 & 4 \\
\hline
\end{array}
\][/tex]
3. Creating the Histogram:
To create the histogram, we plot the frequencies of hours on the y-axis against the hours on the x-axis.
4. Visual Analysis of Symmetry:
To check if a histogram is symmetrical, we need to visually assess if the shape of the histogram on the left side is a mirror image of the shape on the right side. Here's a rough sketch based on the frequency table:
```
Frequency
4 |
3 |
2 |
1 |
0 |_________________
1 7 8 9 (hours)
```
5. Symmetry Check:
- A histogram is symmetrical if both sides of its central point are mirror images of each other. Here, the central point can be considered around values 7.5 to 8.5.
- From the histogram, we observe that the left side consists of hours 1, 7, which have fewer occurrences compared to the right side (which is heavily weighted towards hours 8 and 9). Therefore, the left side doesn't mirror the right side.
6. Final Conclusion:
Given the above observations:
- The histogram is not symmetrical because the distribution of values (especially at hours 8 and 9) is not balanced or mirrored on the opposite side.
Thus, the correct answer is:
The histogram is not symmetrical.
