In the data set below, what are the lower quartile, the median, and the upper qua

lower quartile

Ask by Cook Goodwin. in the United States

Jan 24,2025

Question

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 $$ = $$

UpStudy AI · Accepted Answer

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

lower quartile

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In the data set below, what are the lower quartile, the median, and the upper qua lower quartile