Overview
This lesson covers how to find the lower quartile, upper quartile, range, and interquartile range of a data set, using both step-by-step and formula methods.
Arranging Data
- Always arrange data values from smallest to biggest before any calculations.
Finding the Median
- The median is the middle value of an ordered data set.
Lower Quartile (Q1)
- The lower quartile (Q1) is the median of the lower half of the data (excluding the median if the data set has an odd number of items).
- If two numbers are in the middle, Q1 is the average of those two.
Upper Quartile (Q3)
- The upper quartile (Q3) is the median of the upper half of the data (excluding the median if the data set has an odd number of items).
- If two numbers are in the middle, Q3 is the average of those two.
Mathematical Formula for Quartile Positions
- Lower quartile position: (n + 1) ÷ 4, where n = number of data values.
- Q1 value is at this position in the ordered data set.
- Upper quartile position: 3 × (n + 1) ÷ 4.
- Q3 value is at this position in the ordered data set.
Range & Interquartile Range
- Range = highest value – lowest value.
- Interquartile Range (IQR) = Q3 – Q1.
Key Terms & Definitions
- Median — the middle value in an ordered data set.
- Lower Quartile (Q1) — separates the lowest 25% of data from the rest.
- Upper Quartile (Q3) — separates the highest 25% of data from the rest.
- Range — the difference between the highest and lowest values.
- Interquartile Range (IQR) — the difference between Q3 and Q1.
Action Items / Next Steps
- Practice finding Q1, Q3, range, and IQR for a given data set.
- Review how to use (n + 1)/4 and 3(n + 1)/4 to locate quartile positions.