Let’s analyze the given data step by step to determine the number of clusters, peaks, and investigate the frequency from 4-5.
### Step-by-step Solution:
1. Data Entry and Histogram Creation:
The provided data is:
1, 7, 1, 6, 1, 2, 8, 6, 8, 0
We will first calculate the frequency of each number to create a histogram:
- Frequency of 0: 1
- Frequency of 1: 3
- Frequency of 2: 1
- Frequency of 6: 2
- Frequency of 7: 1
- Frequency of 8: 2
So the histogram looks like this:
[tex]\[
\begin{align*}
0 & : 1 \\
1 & : 3 \\
2 & : 1 \\
6 & : 2 \\
7 & : 1 \\
8 & : 2 \\
\end{align*}
\][/tex]
2. Calculating Clusters:
Clusters are groups of consecutive numbers in the histogram. We analyze the sorted keys: [0, 1, 2, 6, 7, 8]:
- Cluster 1: 0
- Cluster 2: 1, 2
- Gap (indicates the end of the first cluster)
- Cluster 3: 6, 7, 8
Therefore, we have 2 clusters.
3. Calculating Peaks:
Peaks are points where the frequency increases, makes a peak, and then might decrease. Here, we count distinct frequency peaks:
- Peak 1: 1 (Frequency of 1: 3)
- Peak 2: 6 (Frequency of 6: 2)
- Peak 3: 8 (Frequency of 8: 2)
So, we have 3 peaks.
4. Frequency from 4 to 5:
We specifically check if there are any numbers with frequency between 4 and 5:
- 4 is not in the data
- 5 is not in the data
Therefore, there is 0 frequency from 4 to 5.
Based on the analysis, let's check the statements:
- The histogram has [tex]\( \textbf{1 cluster}\)[/tex] – Incorrect.
- The histogram has [tex]\( \textbf{2 clusters}\)[/tex] – Correct.
- The histogram has [tex]\( \textbf{1 peak}\)[/tex] – Incorrect.
- The histogram has [tex]\( \textbf{4 peaks}\)[/tex] – Incorrect.
- The histogram has [tex]\( \textbf{0 frequency from 4-5}\)[/tex] – Correct.
Thus, the correct statements after analyzing the histogram are:
- The histogram has 2 clusters.
- The histogram has 0 frequency from 4-5.
