Short Answer 
The interquartile range (IQR) measures the spread of data, focusing on the middle 50% and minimizing the effect of outliers. To calculate the IQR, determine the first quartile (Q1) and third quartile (Q3), then subtract Q1 from Q3; in the example provided, the IQR is 15 feet.
Step 1: Understand the Interquartile Range
The interquartile range (IQR) is a statistical measure that indicates the spread of a data set while reducing the impact of extreme values or outliers. It is essential for understanding the variability in a set of data, especially when there are significant fluctuations. The IQR is the range within which the middle 50% of the data falls.
Step 2: Calculate Q1 and Q3
To find the IQR, you first need to calculate the two quartiles: Q1 (first quartile) and Q3 (third quartile). Begin by arranging the data points in ascending order. For the example heights of trees: 8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47, the calculations are as follows:
- Q1 is the median of the first half: 16
- Q3 is the median of the second half: 31
Step 3: Compute the Interquartile Range
Once you have both quartiles, you can easily calculate the interquartile range by subtracting Q1 from Q3. Using the Q1 and Q3 values obtained:
- IQR = Q3 – Q1 = 31 – 16
- The interquartile range of the heights of the trees is: 15 feet
This final value gives you a clear indication of the spread of heights without the influence of outliers in the data set.