Short Answer 
The interquartile range (IQR) for Mr. Rubio’s customer data is 10, calculated by subtracting the first quartile (20) from the third quartile (30). The median of the data set is 26, with the organized data ranging from 16 to 34.
Step 1: Organize the Data
Start by organizing the data set of Mr. Rubio’s customers from least to highest. The recorded numbers are:
- 16
- 18
- 20
- 22
- 24
- 26
- 28
- 30
- 30
- 32
- 34
This ensures that you can accurately determine the median and quartiles for further calculations.
Step 2: Calculate the Median and Quartiles
Next, find the median (M) of the data set. With 11 numbers, the median is the 6th value, which is 26. Then, identify the first and third quartiles:
- First quartile (Q1): Evaluate the first half (16, 18, 20, 22, 24) to find its median, which is 20.
- Third quartile (Q3): Evaluate the second half (28, 30, 30, 32, 34) to find its median, which is 30.
Step 3: Compute the Interquartile Range
Finally, calculate the interquartile range (IQR) using the formula: IQR = Q3 – Q1. Substitute the values obtained:
- IQR = 30 – 20 = 10.
This results in an interquartile range of 10, which provides insight into the spread of customer numbers.