Question

the box-and-whisker plot below represents some data set. what percentage of the data values are less than or equal to 25?

Explanation:

Step1: Recall box - whisker plot properties

In a box - and - whisker plot, the whiskers extend to the minimum and maximum values, and the box represents the interquartile range (IQR) with the median inside. The maximum value (the end of the upper whisker or the upper end of the box if there's no upper whisker beyond the box) is relevant here. From the plot, the upper whisker (or the upper boundary related to the data) seems to have a maximum value at 25? Wait, no, looking at the axis, the upper whisker's end is at 25? Wait, the axis has marks at 2,4,6,8,10,12,14,16,18,20,22,24,26. The lower whisker is at around 8, the box goes from lower quartile (Q1) to upper quartile (Q3), and the upper whisker ends at 25? Wait, no, the key point is: in a box - whisker plot, the maximum value (the top of the upper whisker) is the largest data point. But actually, the important thing is that the upper quartile (Q3) and the median and lower quartile (Q1) divide the data into four parts, each representing 25% of the data. Wait, no, the box contains the middle 50% of the data (between Q1 and Q3), the lower whisker (from minimum to Q1) is 25% of the data, and the upper whisker (from Q3 to maximum) is 25% of the data? Wait, no, the correct breakdown is: the minimum to Q1: 25% of the data, Q1 to median: 25% of the data, median to Q3: 25% of the data, Q3 to maximum: 25% of the data. Wait, no, actually, the box - and - whisker plot divides the data into four equal - sized groups (quartiles). So the data is split into four parts, each with 25% of the data. So the minimum to Q1: 25%, Q1 to median: 25%, median to Q3: 25%, Q3 to maximum: 25%. Now, if the maximum value (the end of the upper whisker) is less than or equal to 25, we need to see what part of the data is included. Wait, looking at the plot, the upper whisker's end is at 25? Wait, the axis has 24 and 26, and the upper whisker is at 25? Wait, no, the upper whisker is at 25? Wait, the key is that the maximum data point is at 25 (the end of the upper whisker). So all the data is from the minimum (around 8) to maximum (25). So we need to find what percentage of the data is less than or equal to 25. Since the maximum value is 25, all the data points are less than or equal to 25. Wait, but that can't be. Wait, maybe I misread. Wait, the question is "What percentage of the data values are less than or equal to 25?". In a box - whisker plot, the upper whisker goes to the maximum value. So if the maximum value is 25 (the end of the upper whisker), then all the data (100% of it) is less than or equal to 25. Wait, but let's think again. The box - whisker plot: the four quartiles. The minimum, Q1, median, Q3, maximum. The data is divided into four parts: from min to Q1 (25%), Q1 to median (25%), median to Q3 (25%), Q3 to max (25%). So if the max is 25, then the part from Q3 to max is 25%? No, wait, no. Wait, the total data is 100%. The min to Q1: 25%, Q1 to median: 25%, median to Q3: 25%, Q3 to max: 25%. So if the max is 25, then all data points are ≤25, so the percentage is 100%? Wait, but that seems too easy. Wait, maybe the upper whisker is at 25, meaning that the maximum data point is 25. So all the data is less than or equal to 25. So the percentage is 100%.

Wait, maybe I made a mistake. Let's check the plot again. The vertical axis has marks at 2,4,6,8,10,12,14,16,18,20,22,24,26. The lower whisker is at 8, the box starts at Q1 (let's say around 9) and ends at Q3 (around 23), and the upper whisker ends at 25. So the maximum value is 25. So all the data points are from the minimum (8) to maximum (25). So every data point is less than or equal to 25. So the percentage is 100%.

Step2: Confirm the percentage

Since the maximum value in the data set (represented by the box - whisker plot) is 25 (the end of the upper whisker), all the data values are less than or equal to 25. So the percentage of data values less than or equal to 25 is 100%.

Answer:

100%