Question Type 7: Comparing two different data sets of box and whiskers Exercises

Data set $A$ has the five-number summary: $\min = 2, Q_1 = 5, \text{median} = 8, Q_3 = 10, \max = 20$. Data set $B$ has the five-number summary: $\min = 3, Q_1 = 6, \text{median} = 9, Q_3 = 12, \max = 15$.

Compare the median, range, and interquartile range (IQR) of sets $A$ and $B$. State which set has the higher median, greater range, and larger IQR.

Data set $A$ has a five-number summary: $\text{min} = 10$, $Q_1 = 12$, $\text{median} = 15$, $Q_3 = 18$, $\text{max} = 20$.

If the maximum value in data set $A$ increases from $20$ to $25$, calculate the new range and comment on how the $\text{IQR}$ is affected.

Data set A has a five-number summary: $\text{min} = 1$, $Q_1 = 2$, $\text{median} = 5$, $Q_3 = 8$, $\text{max} = 9$.

Data set B has a five-number summary: $\text{min} = 0$, $Q_1 = 3$, $\text{median} = 6$, $Q_3 = 7$, $\text{max} = 10$.

Based on the positions of the median within the quartiles and whiskers, determine the skewness of each data set.

Data set $A$ has the following five-number summary: $\text{min} = 2$, $Q_1 = 5$, $\text{median} = 8$, $Q_3 = 10$, $\text{max} = 20$.

Identify any outliers in data set $A$ using the $1.5 \times \text{IQR}$ rule.

Data set $A$ has the five-number summary $\text{min} = 4$, $Q_1 = 7$, $\text{median} = 9$, $Q_3 = 13$, $\text{max} = 16$.

Data set $B$ has the five-number summary $\text{min} = 3$, $Q_1 = 6$, $\text{median} = 10$, $Q_3 = 15$, $\text{max} = 20$.

Determine which data set has the larger range.

Data set $A$ has the following five-number summary: $\text{min} = 3, Q_1 = 5, \text{median} = 6, Q_3 = 7, \text{max} = 8$.

Data set $B$ has the following five-number summary: $\text{min} = 8, Q_1 = 10, \text{median} = 12, Q_3 = 14, \text{max} = 16$.

Every value in data set $B$ is decreased by 3. Determine the new five-number summary of data set $B$.

Data set $A$ has five-number summary $\text{min} = 4$, $Q_1 = 7$, $\text{median} = 9$, $Q_3 = 13$, $\text{max} = 16$. If every value in data set $A$ is multiplied by 2, determine the new median, $Q_1$, $Q_3$, range, and $\text{IQR}$.

Data set A has a five-number summary: $\min = 2$, $Q_1 = 5$, $\text{median} = 8$, $Q_3 = 10$, $\max = 12$.

Data set B has a five-number summary: $\min = 3$, $Q_1 = 6$, $\text{median} = 9$, $Q_3 = 12$, $\max = 14$.

Calculate the difference between the medians and interpret which data set has the higher median.

Data set $B$ has the following five-number summary: $\min=3$, $Q_1=6$, $\text{median}=9$, $Q_3=12$, $\max=14$.

Calculate the lower and upper fences using the $1.5 \times \text{IQR}$ rule and determine whether any values would be considered outliers.

Determine which data set has the larger interquartile range ($\text{IQR}$).

Data set $B$ has five-number summary $\text{min} = 8$, $Q_1 = 10$, $\text{median} = 12$, $Q_3 = 14$, $\text{max} = 16$. If $3$ is added to every data point in set $B$, find the new five-number summary.

Data set A has five-number summary $\text{min} = 10$, $Q_1 = 12$, $\text{median} = 15$, $Q_3 = 18$, $\text{max} = 20$. Data set B has $\text{min} = 5$, $Q_1 = 9$, $\text{median} = 14$, $Q_3 = 17$, $\text{max} = 22$.

Calculate the $\text{IQR}$ for both data sets and determine which data set has less variability in the middle $50\%$.