Compare two sets of data using measures of center (mean, median) and spread (range, MAD, IQR).
To compare two data sets, look at both center and spread. The center tells you what is typical; the spread tells you how consistent the values are. Larger spread means more variability.
Mean=number of valuessum of all values
MAD=n∑∣xi−xˉ∣(Mean Absolute Deviation)
IQR=Q3−Q1(Interquartile Range)
🏀Comparing two basketball teams' scores
Team A scores: 88, 90, 91, 89, 92 → Mean = 90, Range = 4
Team B scores: 70, 95, 100, 85, 100 → Mean = 90, Range = 30
Both teams have the same mean, but Team B is far less consistent (larger range).
How to compare two distributions:
1Calculate the mean or median for each group
2Calculate the spread: range, IQR, or MAD
3Write a comparison statement: "Group A typically scored higher/lower and had more/less variability"
4Reference the specific values in your comparison
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Remember This!
Use the median and IQR when data has outliers — they are resistant to extreme values. Use the mean and MAD when data is symmetric with no outliers.
✏️ Try It!
Class A has a mean of 78 and MAD of 5. Class B has a mean of 78 and MAD of 12. Which class has more consistent scores?