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Sagot :
[ 8.2, 8.2, 8.3, 8.3, 8.4, 8.4, 8.5, 8.5, 8.5, 8.7, 8.9 ]
Calculate each component of the five-number summary:
1. Minimum:
The smallest value in the dataset is ( 8.2 ).
2. Maximum:
The largest value in the dataset is ( 8.9 ).
3. Median (Q2):
The median is the middle value of the dataset. Since there are 11 values, the median is the 6th value.
Q2 = 8.4
4. First Quartile (Q1):
The first quartile is the median of the lower half of the data (excluding the overall median if the number of data points is odd). This is the median of the first 5 numbers.
Q1 = 8.3
5. Third Quartile (Q3):
The third quartile is the median of the upper half of the data. This is the median of the last 5 numbers.
Q3 = 8.5
Thus, the five-number summary is:
[tex]{\text{Minimum} = 8.2, \, Q1 = 8.3, \, \text{Median} = 8.4, \, Q3 = 8.5, \, \text{Maximum} = 8.9}[/tex]
By comparing the calculated five-number summary with the options provided, we find that the correct box plot is:
plot with minimum value 8.2, lower quartile 8.3, median 8.4, upper quartile 8.5, and maximum value 8.9
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