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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 3

Lesson 1: Measuring center in quantitative data

# Median in a histogram

Worked example from Khan Academy finding the interval in a histogram containing the media of a data set.

## Video transcript

- [Narrator] 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? And so they're saying is it this interval on the histogram from six 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, nine, seven, three, and two, 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. So two, three, seven, nine, 11. And 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 one, one, three, and a seven. 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 two, this one has nine, 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, see that there. This one has two and this one has two. 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. And so the 24th, 25th, 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 eight hours of sleep.