To calculate the interquartile range (IQR) for the given data set:

Given Data:

$17, 31, 43, 16, 30, 38, 41, 40, 12, 47$

Steps:

Step 1: Organize the data in ascending order.

$12, 16, 17, 30, 31, 38, 40, 41, 43, 47$

Step 2: Find the median (Q2).

• The data set has 10 values (even number of data points).
• The median is the average of the 5th and 6th values.

5th value = 31
6th value = 38

$\text{Median (Q2)} = \frac{31 + 38}{2} = 34.5$

Step 3: Find the lower quartile (Q1).

• Q1 is the median of the lower half of the data:
  $12, 16, 17, 30, 31$
• The median of this set is the 3rd value:
  $Q1 = 17$

Step 4: Find the upper quartile (Q3).

• Q3 is the median of the upper half of the data:
  $38, 40, 41, 43, 47$
• The median of this set is the 3rd value:
  $Q3 = 41$

Step 5: Calculate the interquartile range (IQR).

$IQR = Q3 - Q1 = 41 - 17 = 24$

Final Answer:

The interquartile range (IQR) is 24.

Do you want me to explain any step further or verify with another approach?

Related Questions:

1. What is the significance of the interquartile range in statistics?
2. How would you calculate IQR for an odd-numbered data set?
3. Can the IQR be affected by outliers? Why or why not?
4. What are other measures of variability besides the IQR?
5. How do Q1 and Q3 help visualize the spread of a data set?

Tip: The IQR is often used in boxplots to identify outliers, as values outside $Q1 - 1.5 \cdot IQR$ and $Q3 + 1.5 \cdot IQR$ are considered outliers.