give the five number summary of each set of numbers.
7, 7,5,4,1,9,8,8,8,5,2
To find the five number summary of a set of numbers, you need to determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values. Here's how you can calculate the five number summary for the set of numbers you provided:
Step 1: Sort the numbers in ascending order:
1, 2, 4, 5, 5, 7, 7, 8, 8, 8, 9
Step 2: Find the minimum value:
The smallest number in the set is 1, so the minimum value is 1.
Step 3: Find the first quartile (Q1):
To calculate Q1, we need to find the median of the lower half of the set. Since there are 11 numbers, the lower half consists of the first 5 numbers. The median of these numbers is the average of the middle two values: (2 + 4) / 2 = 3. So, Q1 is 3.
Step 4: Find the median (Q2):
Since there are 11 numbers, the median is the middle value. In this case, the median is 5.
Step 5: Find the third quartile (Q3):
Similar to Q1, we need to find the median of the upper half of the set. The upper half consists of the last 5 numbers. The median of these numbers is (7 + 8) / 2 = 7.5. So, Q3 is 7.5.
Step 6: Find the maximum value:
The largest number in the set is 9, so the maximum value is 9.
Now, we have the complete five number summary:
Minimum: 1
Q1: 3
Median: 5
Q3: 7.5
Maximum: 9