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## Measuring center in quantitative data

Current time:0:00Total duration:2:28

# Median in a histogram

AP Stats: UNC‑1 (EU), UNC‑1.I (LO), UNC‑1.I.3 (EK)

## 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.

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