Question

Find the quartiles for the set of numbers.
86​, 72​, 61​, 91​, 93​, 97​, 77​, 85​, 74​, 75​, 74
Question content area bottom
Part 1
The minimum is
  
61.
Part 2
The maximum is
  
enter your response here.

Answer 1

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**