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

Question

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 \[ \begin{array}{llllll}20 & 32 & 60 & 65 & 71 & 71 \\ 81 & 92\end{array} \]

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Statistics Questions