yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

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.

More Articles

View All
Education as an investment | Careers and education | Financial Literacy | Khan Academy
At a very high level, an investment is when you’re putting, let’s say, your money now into something in the hope that in the future you’re going to get more than that amount of money back. The extra amount that you get back you would call your return on y…
Memories Make Us Who We Are | Breakthrough
Steve believes our identities are built on memory. [Music] When you think about memory, it is the thing that threads and unifies our overall sense of being. So, without it, we become stuck in time, right? And we lose our [Music] identity. But how reliab…
Seth MacFarlane’s Scientific Influences | StarTalk
Seth, I called you into my office. Yes, I gotta talk to you because you want me to help you clean up. I clean up the office. Uh, I got at some point I had to find you and talk to you about the science and Family Guy. Yeah, yeah, you just have to watch a …
Why The Stock Market JUST Dropped
What’s up, Graham? It’s guys you here, and I know I always preach the age-old sayings: don’t time the market, buy and hold; time in the market beats timing the market; the stock market is not the economy; and the market can remain irrational longer than y…
Chaos: The Science of the Butterfly Effect
Part of this video is sponsored by LastPass. More about LastPass at the end of the show. The butterfly effect is the idea that the tiny causes, like a flap of a butterfly’s wings in Brazil, can have huge effects, like setting off a tornado in Texas. Now …
136 Countries Agree To Global Minimum Corporate Tax Rate!
Hey guys, welcome back to the channel! So in this video, we have some interesting news to me. I guess probably a lot of people would zone out at the thought of corporate tax rates, but to me, we have some interesting news. Because last Friday, 136 countr…