Som grae, 12.7 Calouate quarties and intergarcle range voy
In the data set below, what is the interquartile range

Ask by Stephens Barnett. in the United States

Jan 24,2025

Question

Som grae, 12.7 Calouate quarties and intergarcle range voy In the data set below, what is the interquartile range $$ \begin{array}{llllll}20 & 32 & 60 & 65 & 71 & 71 \ 81 & 92\end{array} $$

UpStudy AI · Accepted Answer

To calculate the **interquartile range (IQR)** for the given data set, follow these steps:

**Given Data Set:**
$$ 20, \ 32, \ 60, \ 65, \ 71, \ 71, \ 81, \ 92 $$

**Step 1: Order the Data**
The data is already ordered from smallest to largest.

**Step 2: Find the Median (Q2)**
Since there are 8 data points (an even number), the median is the average of the 4th and 5th values.

$$
\text{Median (Q2)} = \frac{65 + 71}{2} = \frac{136}{2} = 68
$$

**Step 3: Find the First Quartile (Q1)**
Q1 is the median of the first half of the data (the lower 50%).

First half: $$ 20, \ 32, \ 60, \ 65 $$

$$
Q1 = \frac{32 + 60}{2} = \frac{92}{2} = 46
$$

**Step 4: Find the Third Quartile (Q3)**
Q3 is the median of the second half of the data (the upper 50%).

Second half: $$ 71, \ 71, \ 81, \ 92 $$

$$
Q3 = \frac{71 + 81}{2} = \frac{152}{2} = 76
$$

**Step 5: Calculate the Interquartile Range (IQR)**
$$
\text{IQR} = Q3 - Q1 = 76 - 46 = 30
$$

**Conclusion:**
The **interquartile range (IQR)** of the given data set is **30**.
The interquartile range (IQR) is 30.

Som grae, 12.7 Calouate quarties and intergarcle range voy
In the data set below, what is the interquartile range

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