Question Type 6: Finding missing values in a box and whisker plot using given information Exercises

A box and whisker plot has $\min=2$, $Q_1=8$, $\text{median}$ missing, $Q_3=18$, $\max=26$. The median is exactly halfway between $Q_1$ and $Q_3$. Find the median.

In a box and whisker plot the five‐number summary is $\min=4$, $Q_1=10$, $\text{median}=13$, $Q_3$ missing, $\max=25$, and the interquartile range (IQR) is 12. Find the missing $Q_3$.

For a data set the five‐number summary is $\min=3$, $Q_1$ missing, $\text{median}$ missing, $Q_3=21$, $\max=33$. Given $Q_1+Q_3=30$ and the median is the average of $Q_1$ and $Q_3$, find $Q_1$ and the median.

In a data set the five‐number summary is $\min=0$, $Q_1$ missing, $\text{median}=12$, $Q_3$ missing, $\max=48$. The quartiles split the total range into equal thirds. Find $Q_1$ and $Q_3$.

In a box and whisker plot, $Q_1=7$ and the distance from $Q_1$ to the median is 5. The distance from the median to $Q_3$ is twice the distance from $Q_1$ to the median. Find the median and $Q_3$.

A box plot gives $\min=10$, $Q_1=18$, $\text{median}=26$, $Q_3$ missing, $\max$ missing. The interquartile range is 16 and the total range is 30. Find $Q_3$ and $\max$.

For a box plot the five‐number summary is $\min=4$, $Q_1=8$, $\text{median}$ missing, $Q_3$ missing, $\max=28$. The box (from $Q_1$ to $Q_3$) spans one quarter of the total range and is centered around the median. Find the median and $Q_3$.

In a data set the five‐number summary is $\min=6$, $Q_1$ missing, $\text{median}=14$, $Q_3=20$, $\max=30$. The distance from the median to $Q_3$ is 4 units greater than the distance from $Q_1$ to the median. Find $Q_1$.

In a box and whisker plot the five‐number summary is $\min=-2$, $Q_1=5$, $\text{median}=12$, $Q_3=20$, $\max$ missing. The interquartile range equals half the total range. Find the missing $\max$.

In a box plot $\min=4$, $\max$ missing, $Q_1$ missing, $\text{median}=10$, $Q_3$ missing. The distance from the median to $Q_3$ is twice the distance from $Q_1$ to the median, the interquartile range is 6, and the total range is 12. Find $Q_1$, $Q_3$, and $\max$.

A data set has $\min=2$, $\max=22$, $Q_1$ missing, $\text{median}=10$, $Q_3$ missing. The quartiles divide the total range into thirds (i.e.\ $Q_1$ is one‐third and $Q_3$ is two‐thirds of the way from the min to the max). Find $Q_1$ and $Q_3$.

A box and whisker plot has $\min=2$, $\max=18$, $\text{median}=10$. The whiskers (from $\min$ to the median and from the median to $\max$) are equal in length, and the interquartile range is 8. Find $Q_1$ and $Q_3$.