Measures of spread: range, standard deviation and IQR
Two outliers can make your data look perfectly scattered
Range and standard deviation are both pulled hard by extreme values — range uses only the two edges, and standard deviation squares every distance from the mean. The interquartile range (IQR) uses only the middle half, so it barely moves. Add outliers to 20 bus waiting times and watch how each measure reacts.
Dataset viewer20 values
Each dot is one day: minutes waited for the bus. Add up to four extreme days.
20 days, no outliers
01234
Range
7.0
Std dev (÷ n)
1.8
IQR
3.0
Range is the simplest measure of spread — you just subtract the minimum value from the maximum value. While it is easy to calculate and understand, range has a critical weakness: it is completely determined by only two data points, the extremes. If a dataset has 1000 values tightly clustered around the mean but one outlier far away, the range will be huge even though 99.9% of the data shows minimal variation. This makes range useful for understanding the full extent of your data, but unreliable for describing typical spread when outliers are present.
Know This
Standard deviation measures the average distance of data points from the mean in the original units, making it the most informative measure of spread for symmetric distributions without extreme outliers.