Question Type 6: Comparing two different data sets of box and whiskers Exercises

Box plots display the distribution of daily clicks for two marketing campaigns.

• Campaign A: Lower whisker ends at 150, $Q_1 = 200$, $\text{median} = 250$, $Q_3 = 300$, Upper whisker ends at 350.
• Campaign B: Lower whisker ends at 100, $Q_1 = 180$, $\text{median} = 260$, $Q_3 = 290$, Upper whisker ends at 320.

Relative lower-tail variability is defined as the ratio of the length of the lower whisker to the interquartile range (IQR).

Determine which campaign shows greater relative lower-tail variability.

Two box-and-whisker plots show monthly sales (in thousands) for stores X and Y.

Store X: min 50, $Q_1$ 70, median 100, $Q_3$ 130, max 160. Store Y: min 60, $Q_1$ 80, median 105, $Q_3$ 125, max 200.

Which store likely has more frequent extreme high sales, and how can you tell?

Box-and-whisker plots for rainfall (mm) in Region A and Region B show that Region A's lower whisker extends $10 \text{ mm}$ below $Q_1$ while the upper whisker extends $5 \text{ mm}$ above $Q_3$. Region B's whiskers are symmetric, $8 \text{ mm}$ each side of quartiles. Which region has greater skewness and in which direction?

A new observation of $600$ hours is recorded for Machine 2. Determine if this observation is an outlier. Use the $1.5 \times \text{IQR}$ rule.

Two datasets of delivery times (hours) are given below:

• Data set A: 2, 4, 5, 7, 9
• Data set B: 3, 4, 6, 8, 12

Without plotting, compute the five-number summary for each and determine which set has a larger IQR.

Two student groups took different tests. Group A scores: min 30, Q1 45, median 60, Q3 75, max 90. Group B scores: min 20, Q1 50, median 65, Q3 80, max 85. Which group has more consistent performance? Justify using box-and-whisker summaries.

Data set A has minimum 5, first quartile 10, median 15, third quartile 20, and maximum 25. Data set B has minimum 8, first quartile 12, median 18, third quartile 22, and maximum 30. Compare the interquartile ranges and the overall ranges of A and B.

Data set A: $\text{min} = 2$, $Q_1 = 5$, $\text{median} = 9$, $Q_3 = 12$, $\text{max} = 14$. Data set B: $\text{min} = 1$, $Q_1 = 4$, $\text{median} = 7$, $Q_3 = 10$, $\text{max} = 20$. Which distribution is more right-skewed and why?

Two box-and-whisker plots represent daily temperatures in City X and City Y. City X has median $22^\circ\mathrm{C}$ and City Y has median $25^\circ\mathrm{C}$. The IQR of City X is $8^\circ\mathrm{C}$ and that of City Y is $6^\circ\mathrm{C}$. Which city has higher typical temperature, and which has more variability?

Two datasets record systolic blood pressure:

• Dataset A: min 110, Q1 120, median 130, Q3 140, max 150.
• Dataset B: min 100, Q1 115, median 125, Q3 135, max 160.

Which dataset has more extreme high values relative to its IQR?

Data sets of customer wait times (in minutes) are summarized by the following five-number summaries: Data set A: $(5, 10, 15, 20, 25)$ Data set B: $(3, 12, 18, 24, 50)$

Determine the interval of overlap between the intervals defined by the first and third quartiles of the two data sets.