To find the quartiles for the given set of numbers, we will first sort the numbers and then determine the quartiles.
Given numbers:
86, 72, 61, 91, 93, 97, 77, 85, 74, 75, 74
Step 1: Sort the numbers in ascending order.
Sorted:
61, 72, 74, 74, 75, 77, 85, 86, 91, 93, 97
Step 2: Determine the minimum and maximum.
- Minimum: 61
- Maximum: 97
Now, we will find the quartiles.
Step 3: Find the median (Q2).
The median is the middle number in the sorted list. Since there are 11 numbers (an odd count), the median is the middle number:
- The 6th number in the ordered list: 77 (Q2)
Step 4: Find the first quartile (Q1).
Q1 is the median of the first half of the data (the first 6 numbers):
61, 72, 74, 74, 75
- The median of these numbers is: (74 + 74) / 2 = 74 (Q1)
Step 5: Find the third quartile (Q3).
Q3 is the median of the second half of the data (the last 5 numbers):
77, 85, 86, 91, 93, 97
- The median of these numbers is: 86 (Q3)
In summary:
- Minimum: 61
- Maximum: 97
- Q1: 74
- Q2 (Median): 77
- Q3: 86
Therefore, the answers to your questions are:
- Minimum: 61
- Maximum: 97