Integrated Math 1 / Unit 7: Descriptive Statistics
7.1 Measures of Center and Spread
Notes
Center describes a typical value: the mean (sum divided by count) and the median (middle of the ordered data).
- Spread describes variability: range = max $-$ min; IQR = $Q_3 - Q_1$, the spread of the middle half.
- For an even number of values, the median is the mean of the two middle values.
- To find quartiles, split the ordered data at the median; $Q_1$ and $Q_3$ are the medians of the lower and upper halves (leave out the median itself when the count is odd).
- Example: $2, 4, 5, 7, 8, 10, 14$ has median 7, $Q_1 = 4$, $Q_3 = 10$, so IQR $= 6$ and range $= 12$.
Practice
What is the median of $3, 9, 5, 12, 6, 8$?
Ordered: $3, 5, 6, 8, 9, 12$. The middle two are 6 and 8, so the median is $\displaystyle \frac{6 + 8}{2} = 7$.
What is the IQR of $2, 4, 5, 7, 8, 10, 14$?
$Q_1 = 4$ and $Q_3 = 10$, so IQR $= 10 - 4 = 6$.
The yearly salaries (in thousands of dollars) at a small company are $40, 42, 45, 48, 250$. Which measure better describes a typical salary?
The median is 45, a typical value. The mean is 85, which is higher than four of the five salaries.
Ready for more? Take the Unit 7 test.