Find the five-number summary of the following set of numbers.
0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32
To find the five-number summary of a set of numbers, you need to determine the minimum value, the maximum value, the median, and the first and third quartiles. The five-number summary gives you a basic overview of the distribution of the data.
1. Start by ordering the numbers from smallest to largest:
0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32
2. The minimum value is the smallest number in the set, which is 0.08.
3. The maximum value is the largest number in the set, which is 0.32.
4. To find the median, first determine the position of the median. Since there are 10 numbers in the set, the median will be the average of the 5th and 6th numbers. The 5th number is 0.22 and the 6th number is 0.25. Therefore, the median is (0.22 + 0.25) / 2 = 0.235.
5. To find the first quartile (Q1), determine the position of Q1. The first quartile marks the boundary below which 25% of the data falls. There are 10 numbers in the set, so Q1 will be the average of the 3rd and 4th numbers. The 3rd number is 0.18 and the 4th number is 0.20. Therefore, Q1 is (0.18 + 0.20) / 2 = 0.19.
6. To find the third quartile (Q3), determine the position of Q3. The third quartile marks the boundary below which 75% of the data falls. Again, since there are 10 numbers in the set, Q3 will be the average of the 8th and 9th numbers. The 8th number is 0.27 and the 9th number is 0.27 (there is a repeated value). Therefore, Q3 is (0.27 + 0.27) / 2 = 0.27.
Therefore, the five-number summary of the given set of numbers is as follows:
Minimum: 0.08
First Quartile: 0.19
Median: 0.235
Third Quartile: 0.27
Maximum: 0.32