In the data set below, what is the interquartile range $$ \begin{array}{lllllll}32 & 40 & 50 & 51 & 67 & 68 & 97\end{array} $$ Submit

Question

UpStudy AI · Accepted Answer

To determine the **interquartile range (IQR)** of the given data set:

$$ 32, \ 40, \ 50, \ 51, \ 67, \ 68, \ 97 $$

**Step 1: Order the Data**
The data is already in ascending order.

**Step 2: Find the Median (Q2)**
- **Number of data points (n):** 7 (odd)
- **Median (Q2):** 4th value = **51**

**Step 3: Determine the Lower Quartile (Q1)**
- **Lower half:** 32, 40, 50
- **Median of lower half (Q1):** 2nd value = **40**

**Step 4: Determine the Upper Quartile (Q3)**
- **Upper half:** 67, 68, 97
- **Median of upper half (Q3):** 2nd value = **68**

**Step 5: Calculate the IQR**
$$ \text{IQR} = Q3 - Q1 = 68 - 40 = 28 $$

**Answer:**  
The interquartile range is **28**.
The interquartile range is 28.

In the data set below, what is the interquartile range \( \begin{array}{lllllll}32 & 40 & 50 & 51 & 67 & 68 & 97\end{array} \) Submit