Calculate the range, five-number summary (min, Q1, median, Q3, max), interquartile range, and detect outliers — with a box-and-whisker plot
Range = Max − Min
IQR = Q3 − Q1
The five-number summary — Min, Q1, Median, Q3, Max — gives a complete picture of how data is distributed.
Q1 is the median of the lower half of the data. Q3 is the median of the upper half. The IQR (Q3 − Q1) measures the spread of the middle 50% of the data.
The Range (Max − Min) measures total spread from the smallest to largest value.
IQR is more robust to extreme values than range — a single outlier can drastically change the range but barely affects the IQR.
Lower Fence = Q1 − 1.5 × IQR
Upper Fence = Q3 + 1.5 × IQR
Any value below the lower fence or above the upper fence is considered an outlier.
This rule was developed by statistician John Tukey as part of the box plot. It flags values that are unusually far from the middle 50% of the data.
Outliers are important — they may indicate data entry errors, rare events, or genuinely interesting observations worth investigating further.
One-on-one Algebra 1 tutoring builds real intuition for range, IQR, and statistical thinking — so data analysis problems feel straightforward on tests.