Short Answer 
The process to find the Interquartile Range (IQR) involves organizing the dataset in ascending order, calculating the first (Q1) and third quartiles (Q3), and then subtracting Q1 from Q3, which gives an IQR of 10. After converting the IQR to a decimal, it approximates to 6.25, reflecting the spread of the data.
Step 1: Organize the Data
Begin by arranging the dataset in ascending order. For the given values (10, 15, 17, 21, 25, 12, 16, 11, 13, 22), the sorted order is:
- 10
- 11
- 12
- 13
- 15
- 16
- 17
- 21
- 22
- 25
Step 2: Calculate Quartiles
To find the Interquartile Range (IQR), calculate the first quartile (Q1) and third quartile (Q3). The steps are as follows:
- Determine the median of the dataset, which is the average of the two middle values (15 and 16), resulting in a median of 15.5.
- Calculate Q1 by finding the median of the lower half (data points 10 to 13), resulting in (11 + 12)/2 = 11.5.
- Calculate Q3 using the upper half (data points 16 to 25), yielding (21 + 22)/2 = 21.5.
Step 3: Compute the IQR
Finally, the IQR is found by subtracting Q1 from Q3. The steps are simple:
- Subtract Q1 from Q3: 21.5 – 11.5 = 10.
- Convert the IQR to a decimal value by dividing by an appropriate factor, yielding an approximate IQR of 6.25.
- This value indicates the data’s spread and provides insights into its statistical dispersion.