A boxplot shows Q1 = 40, median = 42, Q3 = 70, lower whisker reaching 30, upper whisker reaching 95. What does this tell you about the distribution?
AThe distribution is symmetric — both whiskers extend from the box
BThe distribution is left-skewed — the median is near Q1
CThe distribution is right-skewed — the median is near Q1 and the upper whisker is much longer
DThe distribution is bimodal — the median is not centered in the box
Right skew (positive skew) is signaled by two features acting together: the median sitting close to Q1 (lower edge of the box), indicating most values are packed in the lower half of the IQR, and the upper whisker being much longer than the lower whisker, revealing a tail extending toward high values. Left skew is the mirror: median near Q3 and longer lower whisker. Symmetric distributions have a roughly centered median and roughly equal whisker lengths.
Question 2 Multiple Choice
A dataset has Q1 = 10, Q3 = 20, and a data point at value 40. Should this point be plotted as an outlier?
ANo — 40 is only 20 units above Q3, which is not unusually large
BNo — only the single largest value in the dataset can be an outlier
CYes — the upper fence is Q3 + 1.5 × IQR = 20 + 15 = 35, so 40 exceeds it
DIt depends on whether 40 is the maximum value in the dataset
IQR = Q3 − Q1 = 20 − 10 = 10. Upper fence = Q3 + 1.5 × IQR = 20 + 15 = 35. Since 40 > 35, it is beyond the upper fence and is plotted as an individual outlier dot; the whisker extends only to the most extreme non-outlier (the largest value ≤ 35). The 1.5 × IQR rule determines outlier classification — proximity to Q3 alone is insufficient.
Question 3 True / False
The box in a boxplot always contains exactly 50% of the data values.
TTrue
FFalse
Answer: True
By definition, Q1 is the 25th percentile and Q3 is the 75th percentile, so the middle 50% of observations fall between them — exactly the region spanned by the box. This is a definitional property of quartiles and holds regardless of the distribution's shape. Note that 50% of values (observations) is different from 50% of visual area; in a skewed distribution the box may look asymmetric while still containing exactly half the data.
Question 4 True / False
An outlier flagged by the 1.5 × IQR rule is expected to be an error and should be removed before any analysis.
TTrue
FFalse
Answer: False
The 1.5 × IQR rule identifies unusually extreme values for investigation, not automatic deletion. Outliers can be genuine observations — a legitimately exceptional measurement, a real extreme case, or even the most important finding in the dataset. Whether to remove an outlier requires domain knowledge: Was it recorded correctly? Does the phenomenon naturally produce extremes? Blindly removing outliers inflates apparent precision and can introduce serious bias. The rule's purpose is to flag, not to condemn.
Question 5 Short Answer
How does a boxplot reveal the shape (skewness) of a distribution? What specific features indicate right-skew, left-skew, and symmetry?
Think about your answer, then reveal below.
Model answer: A boxplot reveals skewness through two features: the position of the median line within the box, and the relative lengths of the whiskers. Right skew: median near Q1 (lower box edge) and upper whisker longer than lower. Left skew: median near Q3 (upper box edge) and lower whisker longer than upper. Symmetric: median approximately centered in the box with roughly equal whisker lengths.
These features work together because skewness means values are pulled toward one tail. In a right-skewed distribution, the mass is concentrated at low values (packed near Q1), with the upper whisker stretched toward outlying high values. Boxplots make this pattern immediately visible in a compact, comparable format — especially useful when showing multiple groups side by side.