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

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

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: min = 2, Q1 = 5, median = 9, Q3 = 12, max = 14. Data set B: min = 1, Q1 = 4, median = 7, Q3 = 10, max = 20. Which distribution is more right-skewed and why?

Box-and-whisker plots for rainfall (mm) in Region A and Region B show that Region A’s lower whisker extends 10 mm below Q1 while the upper whisker extends 5 mm above Q3. Region B’s whiskers are symmetric, 8 mm each side of quartiles. Which region has greater skewness and in which direction?

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.

Two box-and-whisker plots show monthly sales (in thousands) for stores X and Y. Store X: min 50, Q1 70, median 100, Q3 130, max 160. Store Y: min 60, Q1 80, median 105, Q3 125, max 200. Which store likely has more frequent extreme high sales, and how can you tell?

Box plots for two machines’ lifetime (in hours) are given by these summaries: Machine 1: min 400, Q1 450, median 480, Q3 510, max 550. Machine 2: min 380, Q1 430, median 500, Q3 520, max 580. An observation of 600 h appears in Machine 2’s data. Is this an outlier? Use 1.5×IQR rule.

Summary of two datasets of delivery times (hours): 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.

Data sets of customer wait times (minutes) have these five-number summaries: A – (5, 10, 15, 20, 25); B – (3, 12, 18, 24, 50). Determine which data set has a more overlapping IQR with the other and compute the overlap interval.

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?

Box plots for two marketing campaigns’ daily clicks: Campaign A has Q1 at 200, median 250, Q3 300; Campaign B has Q1 at 180, median 260, Q3 290. The lower whisker of A is 150, upper whisker 350. B’s whiskers are 100 and 320. Which campaign shows greater relative lower-tail variability?