Overview
This lesson explains how to find the lower quartile, upper quartile, median, range, and interquartile range (IQR) in a dataset, using both manual and formulaic methods.
Ordering Data
- Always arrange dataset values from smallest to largest before calculating quartiles and median.
Finding the Median
- The median is the middle value of an ordered dataset, dividing it into two halves.
- If there are two middle numbers, add them together and divide by 2.
Lower Quartile (Q1)
- The lower quartile (Q1) is the median of the lower half (excluding the overall median if odd number of values).
- If Q1 is between two values, average them; in this example, Q1 = 4.5.
Upper Quartile (Q3)
- The upper quartile (Q3) is the median of the upper half.
- If Q3 is between two values, average them; in this example, Q3 = 9.
Using Formulas for Quartiles
- For Q1 position: (n + 1) ÷ 4, where n = total data points; Q1 is the value at this position.
- For Q3 position: 3 × [(n + 1) ÷ 4]; Q3 is the value at this position.
- If the position is fractional, average the values on either side.
Range and Interquartile Range
- Range = highest value – lowest value; in example: 12 – 3 = 9.
- Interquartile range (IQR) = Q3 – Q1; in example: 9 – 4.5 = 4.5.
Key Terms & Definitions
- Median — the middle value in an ordered dataset.
- Quartile — a value that divides a dataset into four equal parts.
- Lower Quartile (Q1) — the median of the lower half of data.
- Upper Quartile (Q3) — the median of the upper half of data.
- Range — the difference between the highest and lowest values.
- Interquartile Range (IQR) — difference between Q3 and Q1.
Action Items / Next Steps
- Practice finding Q1, Q3, median, range, and IQR on different datasets.
- Review the formula for finding quartile positions using (n + 1) ÷ 4.