Find the five-number summary of the following set of numbers. 0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18,
A) 0.08, 0.18, 0.225, 0.27, 0.28
B) 0.08, 0.16, 0.23, 0.28, 0.32
C) 0.08, 0.18, 0.235, 0.27, 0.32
D) 0.08, 0.18, 0.223, 0.27, 0.32
To find the five-number summary, you need to calculate the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum.
First, let's sort the set of numbers in ascending order:
0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.32
The minimum is the smallest value in the set, which is 0.08.
The maximum is the largest value in the set, which is 0.32.
To find the median (Q2), we need to calculate the average of the two middle values. In this case, the two middle values are 0.20 and 0.22, so the median is (0.20 + 0.22) / 2 = 0.21.
To find the first quartile (Q1), we need to calculate the median of the lower half of the set. In this case, the lower half is {0.08, 0.16, 0.18, 0.20}, so the median of this set is (0.16 + 0.18) / 2 = 0.17.
To find the third quartile (Q3), we need to calculate the median of the upper half of the set. In this case, the upper half is {0.22, 0.25, 0.27, 0.32}, so the median of this set is (0.25 + 0.27) / 2 = 0.26.
Therefore, the five-number summary is: 0.08, 0.17, 0.21, 0.26, 0.32.
Among the answer choices, the correct option is C) 0.08, 0.18, 0.235, 0.27, 0.32, which matches the calculated values.