Question

the box-and-whisker plot below represents some data set. what is the range of the data?

Explanation:

Step1: Identify min and max

From the box - and - whisker plot, the minimum value (left whisker end) is 30 (assuming the left whisker starts at 30, since the scale has 0,20,40... and the left whisker is at 30) and the maximum value (right whisker end) is 80 (right whisker ends at 80). Wait, no, looking at the scale: the left whisker is at 30? Wait, no, the x - axis is from 0 to 100, with marks at 0,20,40,60,80,100. The left whisker is at 30? Wait, no, maybe the left whisker is at 30? Wait, no, let's re - examine. Wait, the left whisker is at 30? Wait, no, the leftmost point (minimum) is 30? And the rightmost point (maximum) is 80? Wait, no, maybe the minimum is 30 and maximum is 80? Wait, no, the range is maximum minus minimum. Wait, looking at the plot, the left whisker starts at 30 (since between 20 and 40, the left whisker is at 30) and the right whisker ends at 80 (between 60 and 80? No, the right whisker is at 80? Wait, the x - axis: 0,20,40,60,80,100. The left whisker is at 30? Wait, no, maybe the minimum is 30 and maximum is 80? Wait, no, let's check again. Wait, the box - and - whisker plot: the left whisker is at 30 (so minimum value \( \text{min}=30 \)) and the right whisker is at 80 (so maximum value \( \text{max}=80 \))? Wait, no, maybe I misread. Wait, the left whisker is at 30? Wait, the x - axis has ticks: 0, then 20, then 40, etc. So the left whisker is at 30 (so min = 30) and the right whisker is at 80 (max = 80)? Wait, no, the range is \( \text{max}-\text{min} \). Wait, maybe the minimum is 30 and maximum is 80? Then range is \( 80 - 30=50 \)? Wait, no, maybe the left whisker is at 30 and right at 80? Wait, let's look at the plot again. The left whisker is at 30 (so the smallest data point is 30) and the right whisker is at 80 (the largest data point is 80). So range is \( 80 - 30 = 50 \)? Wait, no, maybe the minimum is 30 and maximum is 80. So range is \( 80-30 = 50 \). Wait, but maybe I made a mistake. Wait, the x - axis: 0,20,40,60,80,100. The left whisker is at 30 (so min = 30) and right whisker at 80 (max = 80). So range is \( 80 - 30=50 \).

Wait, another way: the box - and - whisker plot's range is calculated as maximum value minus minimum value. From the plot, the leftmost point (minimum) is 30 and the rightmost point (maximum) is 80. So range \( = 80 - 30=50 \).

Step1: Determine min and max

The minimum value (left whisker) is 30, the maximum value (right whisker) is 80.

Step2: Calculate range

Range is defined as \( \text{Range}=\text{Maximum}-\text{Minimum} \). So \( \text{Range}=80 - 30 = 50 \).

Answer:

50