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, 0.28, 0.27
Thank you
put the number in order (least to greatest)
minimum:
Q1:(number that falls between minimum and number less than the Median)
Median:(number that falls in the middle)
Q3: (number that falls between number greater than median and maximum)
Maximum:
Thanks, that helped a great deal.
To find the five-number summary of a set of numbers, you need to compute five values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. Here's how you can find these values for the given set of numbers:
Step 1: Sort the numbers in ascending order:
0.08, 0.16, 0.18, 0.20, 0.22, 0.25, 0.27, 0.27, 0.28, 0.32
Step 2: Find the minimum:
The minimum value is the first number in the sorted list, which is 0.08.
Step 3: Find the first quartile (Q1):
Q1 is the median of the lower half of the data set. Since there are 10 numbers, the lower half consists of the first five numbers. To find Q1, we need to find the median of the first five numbers:
0.08, 0.16, 0.18, 0.20, 0.22
The median of these numbers is 0.18, so Q1 is 0.18.
Step 4: Find the median (second quartile or Q2):
The median is the middle value in the sorted list. Since there are 10 numbers, the middle two numbers are 0.22 and 0.25. To find the median, we take the average of these two numbers:
(0.22 + 0.25) / 2 = 0.235
So the median is 0.235.
Step 5: Find the third quartile (Q3):
Q3 is the median of the upper half of the data set. Again, since there are 10 numbers, the upper half consists of the last five numbers. To find Q3, we need to find the median of the last five numbers:
0.25, 0.27, 0.27, 0.28, 0.32
The median of these numbers is 0.27, so Q3 is 0.27.
Step 6: Find the maximum:
The maximum value is the last number in the sorted list, which is 0.32.
Putting it all together, the five-number summary for the given set of numbers is:
Minimum: 0.08
Q1: 0.18
Median: 0.235
Q3: 0.27
Maximum: 0.32