Question

Find the quartiles for the set of numbers.
89​, 68​, 60​, 92​, 93​, 94​, 81​, 87​, 69​, 77​, 69
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Part 1
The minimum is
  
enter your response here.

Answer 1

To find the quartiles of the given data set, we will first need to sort the data in ascending order. The provided set of numbers is:

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

### Step 1: Sort the Data
Sorting the numbers in ascending order:

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

### Step 2: Find the Minimum
The minimum value in the sorted data set is:

**Minimum = 60**

### Step 3: Find the Quartiles
- **Q1 (First Quartile)** is the median of the first half of the data.
- **Q2 (Second Quartile)** is the median of the entire data set.
- **Q3 (Third Quartile)** is the median of the second half of the data.

#### Finding Q2 (Median)
Since there are 11 numbers (which is odd), the median (Q2) is the 6th number in the sorted set, which is:

**Q2 = 81**

#### Finding Q1
The first half of the data (numbers 1 to 5) is:

60, 68, 69, 69, 77

Q1 is the median of these 5 numbers, which is the 3rd number:

**Q1 = 69**

#### Finding Q3
The second half of the data (numbers 7 to 11) is:

87, 89, 92, 93, 94

Q3 is the median of these 5 numbers, which is the 3rd number:

**Q3 = 92**

### Summary
- Minimum: 60
- Q1: 69
- Q2: 81
- Q3: 92

Please let me know if you need any further assistance!