Question Type 5: Finding missing values in a box and whisker plot using given information Exercises

In a box plot, $\min=2$, $Q_1=4$, $\mathrm{median}=9$, and $\max=25$. The length of the upper whisker is twice the length of the lower whisker. Find the upper quartile $Q_3$.

In a box plot, $Q_1=6$, the median is $15$, and the maximum is $40$. The length of the lower whisker is equal to the difference between the median and $Q_1$. The upper whisker has the same length as the lower whisker. Find the minimum value and $Q_3$.

In a box plot, the quartiles are equally spaced between $\min=5$ and $\max=65$. Find $Q_1$, the median, and $Q_3$.

A box plot has $Q_1 = 10$, $Q_3 = 22$, a lower whisker length of $5$, and an upper whisker length of $9$. Find $\min$ and $\max$.

A box plot has a lower whisker at $3$, a median at $10$, an upper quartile $Q_3 = 17$, and an upper whisker at $25$. The interquartile range (IQR) is $12$. Find the lower quartile $Q_1$.

In a box plot, $\min=0$, $\text{median}=50$, and $\max=100$. The interquartile range equals one-third of the total range, and the distances from the median to $Q_1$ and $Q_3$ are equal. Find $Q_1$ and $Q_3$.

A box plot has $\min=12$ and $\max=72$. The quartiles $Q_1$ and $Q_3$ divide the total range into three equal parts. Find $Q_1$ and $Q_3$.

A box plot has five-number summary distances of $6$, $12$, $18$, and $24$ between successive points, starting at $\min=3$. Find $Q_1$, the median, $Q_3$, and $\max$.

A box plot has $\min=5$, $\text{median}=15$, $Q_3=24$, and $\max=30$. The IQR is three-quarters of the total range. Find the lower quartile $Q_1$.

In a box plot, the distances from $Q_1$ to the median and from the median to $Q_3$ are equal, and the interquartile range is $20$. The median is $50$. Find $Q_1$ and $Q_3$.

In a box plot, $Q_1=25$, $Q_3=55$, and the lower whisker length is $20\%$ of the total range. The maximum is $85$. Find the minimum. (Total range $= \text{max} - \text{min}$.)

A box plot has $\min = 2$, $\text{median} = 8$, $Q_3 = 14$, and $\max$ unknown, and $Q_1$ unknown. The four intervals between the five-number summary are in the ratio $1:2:3:4$. Find $Q_1$ and $\max$.