Step 1:

Sort the data in ascending order:  

\[10, 11, 12, 13, 15, 16, 17, 21, 22, 25\]

Step 2:

Find the median (Q2):  

Since there are 10 data points, the median is the average of the 5th and 6th values: 
\[Q2 = \frac { 15 + 16} { 2} = 15.5\]

Step 3:

Find the first quartile (Q1): 
The first quartile is the median of the first half of the data (the first 5 values): 
\[Q1 = \text { median of } 10, 11, 12, 13, 15 = 12\]

Step 4:

Find the third quartile (Q3):  

The third quartile is the median of the second half of the data (the last 5 values): 
\[Q3 = \text { median of } 16, 17, 21, 22, 25 = 21\]

Step 5:

Calculate the IQR:  

\[\text { IQR} = Q3 - Q1 = 21 - 12 = 9\]

Step 6:

None of the provided options exactly match the computed IQR of 9. However, based on the provided options, the closest match would be: d) 9.50

Supplemental Knowledge:

Interquartile Range (IQR) is a measure of statistical dispersion calculated as the difference between third quartile (Q3) and first quartile (Q1) values, representing where 50% or more data points fall in any given sample set.To find the IQR, follow these steps:

1. Order the Data: 

Arrange the data in ascending order. 
2. Find Q1 and Q3:

- Q1 is the median of the first half of the data. 
- Q3 is the median of the second half of the data. 
3. Calculate IQR: 

Subtract Q1 from Q3.

From Concepts to Reality:

Understanding IQR can be extremely useful across numerous fields such as finance, research and quality control. Financial analysts could utilize it to understand stock price volatility by measuring how prices spread around their median value; in quality control applications however manufacturers could utilize IQR measurements of product consistency by tracking variations in dimensions or features of their products.

Need more help with statistics or other mathematical concepts? UpStudy’s Statistics and Probability Calculator can assist you with all your statistical calculations and much more! With UpStudy’s comprehensive tools and expert guidance, mastering these concepts becomes straightforward and enjoyable. Check out our calculators today for all your mathematical needs!