Let's break down the solution step-by-step based on the histogram data provided:
1. Data Input:
The given data for the histogram is: 9, 1, 8, 7, 9, 9, 8, 9, 8, 7.
2. Frequency Distribution:
We need to determine how frequently each value appears in the data set:
- 9 appears 4 times
- 1 appears 1 time
- 8 appears 3 times
- 7 appears 2 times
Thus, the frequency distribution is:
[tex]\[
[(1, 1), (7, 2), (8, 3), (9, 4)]
\][/tex]
3. Mode Value:
The mode is the value that appears the most frequently.
- In this case, 9 appears 4 times, which is the highest frequency.
So, the mode value is:
[tex]\[
9
\][/tex]
4. Checking Symmetry:
To check for symmetry, we need to compare the left side of the data to the right side.
- First, split the data into two halves:
[tex]\[
\text{Left side: } [9, 1, 8, 7, 9]
\][/tex]
[tex]\[
\text{Right side: } [9, 8, 9, 8, 7]
\][/tex]
- Reverse the right side:
[tex]\[
\text{Reversed right side: } [7, 8, 9, 8, 9]
\][/tex]
- Compare the left side to the reversed right side. If they are identical, the histogram is symmetric.
[tex]\[
\text{Left side: } [9, 1, 8, 7, 9]
\][/tex]
[tex]\[
\text{Reversed right side: } [7, 8, 9, 8, 9]
\][/tex]
These two arrays are not the same. Therefore, the histogram is not symmetrical.
5. Conclusion:
- The frequency distribution of the given data is [tex]\([(1, 1), (7, 2), (8, 3), (9, 4)]\)[/tex].
- The mode value is 9.
- The histogram is not symmetrical.
So, the correct answer is:
[tex]\[
\text{The histogram is not symmetrical.}
\][/tex]
