Knowledge Organiser: Range and Interquartile Range (IQR)
Key Terms
- Range: Total spread of data (highest − lowest)
- Quartile: A value that divides ordered data into four equal parts
- Q1 (Lower Quartile): 25% of data lies below this value
- Q2 (Median): 50% of data lies below this value
- Q3 (Upper Quartile): 75% of data lies below this value
- IQR: Interquartile range: spread of the middle 50% of data
Must-Know Facts
- Always sort data into ascending order before finding quartiles
- Range is affected by outliers; IQR is not
- IQR is always less than or equal to the range
- A smaller IQR means data is more consistent (less spread)
- A larger IQR means data is more variable
- Use IQR when comparing consistency between two datasets
- IQR and range share the same units as the original data
Key Formulas
- Range = highest value − lowest value
- IQR = Q3 − Q1
- Q1 = median of the lower half of data
- Q3 = median of the upper half of data
Common Mistakes
- Not ordering data first: Always sort data in ascending order before finding quartiles or range
- Including the median in quartile halves: For an odd number of values, exclude the median when finding Q1 and Q3
- Range vs IQR: Range uses only the highest and lowest values (affected by outliers); IQR uses only the middle 50% (more reliable)
- IQR = Q3 − Q1, not Q3 ÷ Q1: Subtract the lower quartile from the upper quartile