Question

Find the quartiles for the set of numbers.
89​, 68​, 60​, 92​, 93​, 94​, 81​, 87​, 69​, 77​, 69
Question content area bottom
Part 1
The minimum is
  
60.
Part 2
The maximum is
  
94.
Part 3
The second quartile is
  
81. ​(Simplify your​ answer.)
Part 4
The first quartile is
  
69. ​(Simplify your​ answer.)
Part 5
The third quartile is
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

To find the quartiles for the given set of numbers, we start by sorting the data in ascending order. The provided numbers are:

89, 68, 60, 92, 93, 94, 81, 87, 69, 77, 69.

Now, let's arrange them in ascending order:

60, 68, 69, 69, 77, 81, 87, 89, 92, 93, 94.

Next, we need to find the quartiles:

1. **Minimum**: Confirmed as 60.
2. **Maximum**: Confirmed as 94.
3. **Second Quartile (Q2)**: This is the median of the dataset.

There are 11 numbers (odd), so the median will be the middle number, which is the 6th number in the sorted list.

**Median (Q2)** = 81.

4. **First Quartile (Q1)**: This is the median of the first half of the data (the lower half):

The lower half consists of the first 5 numbers: 60, 68, 69, 69, 77.

The median of this half (5 numbers - odd) is the 3rd number:

**Q1** = 69.

5. **Third Quartile (Q3)**: This is the median of the second half of the data (the upper half):

The upper half consists of the last 5 numbers: 81, 87, 89, 92, 93, 94.

The median of this half (5 numbers - odd) is the 3rd number:

**Q3** = 89.

In summary:
- Minimum is 60.
- Maximum is 94.
- Second quartile (Q2) is 81.
- First quartile (Q1) is 69.
- Third quartile (Q3) is 89.

So, the final answer for Part 5 (the third quartile) is **89**.