Step 1:

First, order the data set from least to greatest: 

1, 2, 3, 6, 7, 7, 7, 8, 9. 
 

Step 2:

Find the median (Q2): 

The middle value is 7. 
 

Step 3:

Find the first quartile (Q1): 

The median of the first half (1, 2, 3, 6) is 2.5. 
 

Step 4:

Find the third quartile (Q3): 

The median of the second half (7, 7, 8, 9) is 7.5. 
 

Step 5:

Calculate the interquartile range (IQR):  
\(\text { IQR} = Q3 - Q1 = 7.5 - 2.5 = 5\)
 

Step 6:

Therefore, the interquartile range is 5.

Supplemental Knowledge:

Interquartile range (IQR) is a statistical measure that measures dispersion among data points in an array. IQR can be calculated as the difference between first quartile Q1 and third quartile Q3. Q1 refers to medians from lower half data set while Q3 represents upper half medians.

To find Q1 and Q3:

1. Arrange the data in ascending order.

2. Find the median (the middle value).

3. Divide the data into two halves: values below and above the median.

4. Find the medians of these two halves to get Q1 and Q3.

Concepts to Actions:

Understanding IQR can be extremely useful in many real-life settings, from quality control in manufacturing to monitoring production quality through product dimensions measurements. Calculating an IQR helps identify how consistent your products are - smaller values indicate most have dimensions close together while larger numbers indicate increased variability between items produced.

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