Overview
This lecture covers how to measure data spread for skewed distributions using the Interquartile Range (IQR), including its definition, calculation steps, and interpretation.
Shape and Center of Data
- The shape of a data set (symmetric or skewed) determines which center measure to use.
- Use the mean for symmetric data and the median for skewed data.
Measuring Spread
- Knowing only the center is not enough; data spread is also important.
- For symmetric data, use standard deviation to measure spread.
- For skewed data, use the interquartile range (IQR).
Interquartile Range (IQR)
- IQR represents the range of the middle 50% of data values.
- To find IQR:
- Step 1: Find the median to split data into lower and upper 50%.
- Step 2: Find Q1 (median of the lower 50%) and Q3 (median of the upper 50%).
- IQR = Q3 - Q1.
- Example: For data 19, 20, 24, 27, 28, 30
- Median = 25.5
- Q1 = 20 (median of 19, 20, 24)
- Q3 = 28 (median of 27, 28, 30)
- IQR = 28 - 20 = 8
Calculator Use
- Calculators can provide Q1 and Q3 but do not directly calculate IQR.
- Always subtract the smaller value (Q1) from the larger (Q3); IQR must be positive.
Interpreting IQR
- IQR is interpreted as the range of the middle 50% of data (e.g., quiz scores differ by 8 points).
- The unit for IQR matches the data (e.g., tons per person).
Key Terms & Definitions
- Median — Value that splits data so 50% are below and 50% are above.
- Quartile 1 (Q1) — Median of the lower 50% of data.
- Quartile 3 (Q3) — Median of the upper 50% of data.
- Interquartile Range (IQR) — The difference Q3 - Q1; shows spread of the middle 50%.
Action Items / Next Steps
- Complete example four: Find and interpret IQR for provided Q1 and Q3 values.
- Practice identifying when to use mean/standard deviation versus median/IQR based on data shape.