Answer:
10
Step-by-step explanation:
To determine which measure of center best represents the data, we can consider the mean, median, and mode. Let's calculate each of these for the given set of data:
Data: {9, 7.50, 10, 10, 14.75, 10, 8.50, 7.75, 10}
1. Mean (Average):
[tex] \textsf{Mean} = \dfrac{\textsf{Sum of all values}}{\textsf{Number of values}} [/tex]
[tex] \textsf{Mean} = \dfrac{9 + 7.50 + 10 + 10 + 14.75 + 10 + 8.50 + 7.75 + 10}{9} [/tex]
[tex] \textsf{Mean} \approx \dfrac{87.5}{9} [/tex]
[tex] \textsf{Mean} \approx 9.72222222 [/tex]
2. Median:
Arrange the data in ascending order:
[tex] 7.50, 7.75, 8.50, 9, 10, 10, 10, 14.75 [/tex]
The median is the middle value, which is 10 in this case.
3. Mode:
The mode is the value that appears most frequently. In this dataset, 10 appears three times, making it the mode.
Considering these measures:
- Mean: 9.7222
- Median: 10
- Mode: 10
The dataset has some variability, and the mean might be affected by the larger value (14.75). However, since the median and mode are both 10, which is the most frequent value, they might be more representative of the central tendency in this case.
Therefore, the median and mode best represent the center of this data which is 10.
