Integrated Math 1 / Unit 7: Descriptive Statistics
7.3 Data Displays and Shape
Notes
Different displays show different features of one-variable data.
- Dot plot: one dot per value. Histogram: bars for intervals. Box plot: five-number summary (min, $Q_1$, median, $Q_3$, max).
- Shape: symmetric, skewed right (long tail to the right), or skewed left. In a right-skewed set the mean is greater than the median.
- Outlier rule: a value is an outlier if it is below $Q_1 - 1.5 \cdot \text{IQR}$ or above $Q_3 + 1.5 \cdot \text{IQR}$.
- Example: $Q_1 = 20$ and $Q_3 = 50$ give IQR $= 30$ and upper fence $50 + 45 = 95$.
Practice
A data set has $Q_1 = 20$ and $Q_3 = 50$. Using the $1.5 \cdot \text{IQR}$ rule, is a value of 100 an outlier?
IQR $= 30$, so the upper fence is $50 + 1.5(30) = 95$. Since $100 > 95$, it is an outlier.
A histogram has a long tail stretching to the right. Which statement is most likely true?
Right-skewed data have a few large values that pull the mean above the median.
Which display shows the five-number summary of a data set?
A box plot is built from the minimum, $Q_1$, median, $Q_3$ and maximum.
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