In the data set below, what are the lower quartile, the median, and the upper qua $$ 32 \quad 35 \quad 62 \quad 73 \quad 32 $$ lower quartile $$ = $$

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To determine the lower quartile, median, and upper quartile of the given data set, follow these steps:

### **Given Data Set:**
$$ 32, \quad 35, \quad 62, \quad 73, \quad 32 $$

### **Step 1: Sort the Data**
First, arrange the data in ascending order:
$$ 32, \quad 32, \quad 35, \quad 62, \quad 73 $$

### **Step 2: Find the Median**
The median is the middle value of the sorted data.
- **Number of data points (n):** 5 (which is odd)
- **Median position:** $$ \frac{n + 1}{2} = \frac{5 + 1}{2} = 3^{\text{rd}} $$ position

So, the **median** is:
$$ \text{Median} = 35 $$

### **Step 3: Find the Lower Quartile (Q1)**
The lower quartile is the median of the lower half of the data (excluding the overall median).

- **Lower half data:** 32, 32
- **Number of data points in lower half:** 2
- **Lower Quartile position:** Since there are an even number of data points, it's the average of the two middle numbers.
  
So, the **lower quartile (Q1)** is:
$$ Q1 = \frac{32 + 32}{2} = 32 $$

### **Step 4: Find the Upper Quartile (Q3)**
The upper quartile is the median of the upper half of the data (excluding the overall median).

- **Upper half data:** 62, 73
- **Number of data points in upper half:** 2
- **Upper Quartile position:** Similar to the lower quartile, it's the average of the two middle numbers.
  
So, the **upper quartile (Q3)** is:
$$ Q3 = \frac{62 + 73}{2} = 67.5 $$

### **Summary:**
- **Lower Quartile (Q1) = 32**
- **Median = 35**
- **Upper Quartile (Q3) = 67.5**

However, if you prefer to keep quartiles as actual data points without averaging (common in some contexts), you might consider:
- **Upper Quartile (Q3) = 62**

But based on typical calculations involving averages for quartiles with even subsets:

**Lower quartile = 32, median = 35, and upper quartile = 62.**
Lower quartile = 32, median = 35, upper quartile = 62

In the data set below, what are the lower quartile, the median, and the upper qua \( 32 \quad 35 \quad 62 \quad 73 \quad 32 \) lower quartile \( = \)

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