How to Draw and Read a Box Plot

The ends of the whiskers show the smallest and largest values: the left whisker ends at 20 and the right whisker ends at 80.

Range = largest − smallest = $80-20=60$.

The box itself runs from 30 to 60; that gives the interquartile range of 30, not the range. Read the value at each whisker end from the scale rather than counting tick marks, and remember to subtract: the maximum on its own (80) is not the spread.

The two ends of the box are the quartiles: the lower quartile $Q_1=30$ and the upper quartile $Q_3=60$.

IQR = $Q_3-Q_1=60-30=30$.

Do not use the whiskers: $80-20=60$ is the full range. The line inside the box, at 50, is the median, not a quartile. And read the two quartile values off the scale rather than counting the tick marks across the box.

The median is shown by the line drawn inside the box. The edges of the box are the quartiles, not the median.

That line sits directly above the 50 mark on the scale, so the median is 50.

The box runs from $Q_1=30$ to $Q_3=60$, and the whiskers reach the smallest value, 20, and the largest, 80. Take care with the scale as well: the ticks are 10 apart, and the first tick is 10, not 0.

The box itself shows the middle $50\%$ of the data: it runs from the lower quartile $Q_1$ to the upper quartile $Q_3$.

Here the box starts at 30 and ends at 60, so the middle $50\%$ lies between 30 and 60.

The whisker ends, 20 and 80, are the minimum and maximum, and the line at 50 inside the box is the median.

A box plot splits the data into four equal quarters, and each quarter holds $25\%$ of the values: minimum to $Q_1$, $Q_1$ to the median, the median to $Q_3$, and $Q_3$ to the maximum.

From $Q_1$ (30) up to the maximum (80) covers three of those quarters, so the percentage is $3\times 25\%=75\%$.

The sections are different lengths on the page, but each one still holds the same amount of data.

There are 7 values and they are already in order: 10, 20, 35, 40, 45, 70, 80.

The median is the middle (4th) value, so the median is 40.

The lower half, the three values below the median, is 10, 20, 35, so $Q_1=20$. The upper half is 45, 70, 80, so $Q_3=70$.

The smallest value is 10 and the largest is 80, so the box plot is: Min 10, $Q_1$ 20, median 40, $Q_3$ 70, Max 80. The box goes from $Q_1$ to $Q_3$, not from the smallest value to the largest, and the four sections come out different widths. That is fine, as each still contains a quarter of the data.