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Median in a histogram | Summarizing quantitative data | AP Statistics | Khan Academy

2m read
·Nov 11, 2024

Miguel tracked how much sleep he got for 50 consecutive days and made a histogram of the results. Which interval contains the median sleep amount? So, they're saying, is it this interval on the histogram from 6 to 6.5, or this one, or this one, or any of these? Which of these intervals contain the median? Pause this video and see if you can figure that out.

All right, now let's work through this together and let's just remind ourselves how we find the median. If I had the data points 11, 9, 7, 3, and 2, the way that we find the median is we can order it from least to greatest. Or actually, you could do it from greatest to least, but let's do least to greatest: 2, 3, 7, 9, 11. The median would be the middle number, and I have a clear middle number because I have five data points.

If I have an even number of data points, I still would want to order them from least to greatest. So let's say that I have a 1, 1, 3, and a 7. But here, you don't have a clear middle, so the median would be the mean of the middle two numbers. So in this situation, Miguel has an even number of data points, so the median would be the mean of the 25th and 26th data point. These would be the middle two data points.

So, which interval here contains the 25th and the 26th data point? Well, we can start at the bottom. So, we have—actually, let's just look at each interval and think about how many data points they have in it. This one has 2, this one has 9, this one has 12, and I'm just reading out how many data points there are in each of these intervals. This one has 12, this one has 11. I see that there—this one has 2, and this one has 2.

So if we look at just this, we have the two lowest. If we look at the two bottom intervals combined, we have the 11 lowest. If we look at the three bottom intervals, we have the 11 plus 12, you have the 23 lowest. So this is the 23 lowest data points. The 24th, 25th, and 26th—the next 12 data points starting from the bottom, starting from the lowest, are going to be in this next interval here.

And we care about the 25th and the 26th, so they're definitely going to be in this interval from 7.5 hours of sleep to 8 hours of sleep.

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