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

For a data set, the five-number summary is given by: $\min=3, Q_1, \text{median}, Q_3=21, \max=33$.

Given that $Q_1 + Q_3 = 30$ and the median is the average of $Q_1$ and $Q_3$, find the value of $Q_1$ and the median.

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 $Q_3$.

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

A symmetric box and whisker plot has $\min=2$, $\max=18$, and $\text{median}=10$. The interquartile range is 8.

Find the value of $Q_1$ and $Q_3$.

For a box plot, the five-number summary is $\min = 4$, $Q_1 = 8$, median missing, $Q_3$ missing, and $\max = 28$. 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 box-and-whisker plot, the five-number summary is given by: $\text{min} = 4$, $Q_1 = 10$, $\text{median} = 13$, $Q_3$ is missing, and $\text{max} = 25$.

Given that the interquartile range (IQR) is 12, find the value of $Q_3$.

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

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. [2 marks]

A data set has a minimum value of $2$ and a maximum value of $22$. Two points, $P_1$ and $P_2$, divide the total range into three equal parts such that $P_1$ is one-third of the way from the minimum to the maximum and $P_2$ is two-thirds of the way from the minimum to the maximum.

Find the values of $P_1$ and $P_2$.

In a data set, the five-number summary is $\min = 0$, $Q_1$ missing, $\text{median} = 24$, $Q_3$ missing, and $\max = 48$. The quartiles $Q_1$ and $Q_3$ split the total range into equal thirds. Find the values of $Q_1$ and $Q_3$.

In a data set, the five-number summary is $\min = 6$, $Q_1$ is missing, $\text{median} = 14$, $Q_3 = 20$, and $\max = 30$. 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 plot, $\min = 4$, $\text{median} = 10$, and the values for $Q_1, Q_3$, and $\max$ are 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 $\max$.