Statistics / Unit 2: Describing Distributions
2.2 Range, Quartiles and IQR
Notes
Measures of spread describe how far apart the values are.
- Range $=$ maximum $-$ minimum.
- Split the ordered data at the median. Q1 is the median of the lower half and Q3 is the median of the upper half. When $n$ is odd, leave the overall median out of both halves.
- IQR $= Q_3 - Q_1$ is the spread of the middle $50\%$ of the data.
- The five-number summary is minimum, $Q_1$, median, $Q_3$, maximum.
- Example: 2, 4, 6, 8, 10, 12, 14 has $Q_1 = 4$, median 8, $Q_3 = 12$, so IQR $= 8$ and range $= 12$.
Practice
What is the range of 14, 22, 9, 31, 18?
$31 - 9 = 22$.
For the data 3, 5, 7, 9, 11, 13, 15, 17, what is the IQR?
$\displaystyle Q_1 = \frac{5 + 7}{2} = 6$ and $\displaystyle Q_3 = \frac{13 + 15}{2} = 14$, so IQR $= 14 - 6 = 8$.
The IQR describes the spread of:
IQR $= Q_3 - Q_1$ covers the middle $50\%$.
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