Question

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

Explanation:

Step1: Recall box - and - whisker plot components

In a box - and - whisker plot, the left - most whisker (or the left end of the plot) represents the minimum value of the data set.

Step2: Identify the minimum value from the plot

Looking at the given box - and - whisker plot, the left end of the whisker is at the value of 84? Wait, no, wait. Wait, the number line has 81, 84, 87, 90, 93. Wait, the left whisker starts at 84? Wait, no, looking at the plot, the leftmost vertical line (the start of the left whisker) is at 84? Wait, no, maybe I misread. Wait, the number line: 81, then some ticks, then 84, then some ticks, then 87, then some ticks, then 90, then some ticks, then 93. Wait, the left whisker's left end is at 84? Wait, no, wait the plot: the left vertical line (the minimum) is at 84? Wait, no, maybe I made a mistake. Wait, no, let's check again. Wait, the box - and - whisker plot: the left whisker extends from the minimum to the first quartile. The leftmost point (the minimum) is the left end of the left whisker. From the number line, the left end of the left whisker is at 84? Wait, no, wait the number line has 81, then 84 is the next major tick. Wait, maybe the left end is 84? Wait, no, maybe I misread. Wait, the problem's plot: the left vertical line (the minimum) is at 84? Wait, no, let's see the number line: 81, then three small ticks, then 84, then three small ticks, then 87, then three small ticks, then 90, then three small ticks, then 93. The left whisker starts at 84? Wait, no, the leftmost vertical line (the minimum) is at 84? Wait, no, maybe the left end is 84. Wait, no, maybe I made a mistake. Wait, no, the minimum value in a box - and - whisker plot is the leftmost data point, which is the end of the left whisker. From the plot, the left end of the left whisker is at 84? Wait, no, wait the number line: 81 is the first major tick, then 84, 87, 90, 93. The left whisker's left end is at 84? Wait, no, maybe the left end is 84. Wait, no, let's check again. Wait, the plot shows that the left whisker starts at 84? Wait, no, the left vertical line (the minimum) is at 84. Wait, maybe I was wrong earlier. Wait, the number line: 81, then 84 is the next. So the minimum value is 84? Wait, no, wait the leftmost line (the minimum) is at 84. Wait, yes, because the left whisker starts at 84. Wait, no, maybe the left end is 84. Wait, let's confirm: in a box - and - whisker plot, the minimum is the smallest value, represented by the left end of the left whisker. From the given plot, the left end of the left whisker is at 84? Wait, no, the number line has 81, but the left whisker starts at 84? Wait, maybe the plot's left end is 84. Wait, maybe I misread the number line. Let me check again. The number line: 81, then three small intervals, then 84, then three small intervals, then 87, then three small intervals, then 90, then three small intervals, then 93. The left whisker's left end is at 84. So the minimum value is 84? Wait, no, wait the leftmost vertical line (the minimum) is at 84. So the minimum value of the data is 84? Wait, no, maybe I made a mistake. Wait, no, the left end of the left whisker is the minimum. So from the plot, the left end is at 84. So the minimum value is 84. Wait, but let's check the number line again. 81 is a major tick, then 84. So maybe the left end is 84. So the minimum value is 84.

Answer:

84