To construct a box plot, we first need to identify the five-number summary of the given data set: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
The data set is: 10, 12, 15, 21, 24, 30
- Minimum: The smallest value in the data set, which is 10.
- Maximum: The largest value in the data set, which is 30.
- Median (Q2): The median is the middle value. Since there are 6 numbers (even count), we take the average of the two middle numbers (15 and 21): \[(15 + 21) / 2 = 18.\]
- First Quartile (Q1): The first quartile is the median of the lower half of the data (10, 12, 15). The median of these three numbers is 12.
- Third Quartile (Q3): The third quartile is the median of the upper half of the data (21, 24, 30). The median of these three numbers is 24.
Thus, the five-number summary is:
- Minimum: 10
- Q1: 12
- Median (Q2): 18
- Q3: 24
- Maximum: 30
In a box plot, the letter A typically represents Q1, which is the value at the first quartile.
Therefore, the value represented by the letter A is 12.
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