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Video: Interpreting a Double Box-And-Whisker Plot

Tim Burnham

The double box-and-whisker plot shows the average number of sunny days for two cities. What percent of the data for City 1 is above the median for City 2?<Figure>

03:40

Video Transcript

The double box and whisker plot shows the average number of sunny days for two cities. What percent of the data for City One is above the median for City Two?

Well, let’s just think about how to interpret our box plot. This value here tells us the maximum number of sunny days that City Two got, so we can see that one year it had three hundred and fifty sunny days. And this value here tells us the minimum, so we can see that one year City Two had only a hundred and twenty five sunny days. Now if we put all of the pieces of data that we had for City Two and plotted them, we’ll find that twenty five percent of those data points would be in this region here. That means that a quarter of the time, that city has between a hundred and twenty five and two hundred and fifty days of sunshine. And we call the start of the box here, the lower quartile. And twenty five percent of the data points are between the minimum and the lower quartile. As we said, in City Two, a quarter of the time or twenty five percent of the time, they have between the minimum and the lower quartile, that’s a hundred and twenty five and two hundred and fifty days of sunshine.

If we carry on plotting those points, another twenty five percent of our data points would be between these two values. The line in the middle of our box marks the median. That’s the middle point of our data because twenty five percent plus twenty five percent, that’s fifty percent of years we’re going to have less than the median, that’s two hundred and seventy five days of sunshine in City Two.

Plotting some more data points, a quarter of them will be in this range. And that means that three-quarters of the time, seventy five percent of the time, we’re going to have three hundred or fewer days of sunshine in City Two. We call three hundred the upper quartile because three-quarters of the time we’re gonna have less than that number of days of sunshine. So the remaining twenty five percent of data points fall in this range. That means in a quarter of the years that we looked at, or twenty five percent of them, City Two got between three hundred and three hundred and fifty days of sunshine.

Right. Now we’ve checked that we know what a box and whisker plot tells us. Let’s go back to the question. What percent of the data for City One is above the median for City Two? Well, City Two’s median, we said here, was two hundred and seventy five. So for City Two, half the time they have more than two hundred and seventy five days of sunshine, and half the time they have less than two hundred and seventy five days of sunshine. So fifty percent of the data for City Two is above the median. But, we want to know what percent of City One data is above that value, two hundred and seventy five days of sunshine. Now that range for City One maps between the upper quartile and the maximum, which means that only a quarter of the time, twenty five percent of the time, do we have more than two hundred and seventy five days of sunshine in City One.

So our answer is: twenty five percent of the data for City One is above the median for City Two. Remember, the median number of days sunshine for City Two was two hundred and seventy five. And in twenty five percent of years, City One gets more than that two hundred and seventy five days of sunshine.