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

Comparing with z-scores | Modeling data distributions | AP Statistics | Khan Academy


2m read
·Nov 11, 2024

Before applying to law school in the U.S., students need to take an exam called the LSAT. Before applying to medical school, students need to take an exam called the MCAT. Here are some summary statistics for each exam.

For the LSAT, the mean score is 151 with a standard deviation of 10. For the MCAT, the mean score is 25.1 with a standard deviation of 6.4. Juwan took both exams; he scored 172 on the LSAT and 37 on the MCAT. Which exam did he do relatively better on?

So pause this video and see if you can figure it out. The way I would think about it is you can't just look at the absolute score because they are on different scales and they have different distributions. But we can use this information.

If we assume it's a normal distribution, or relatively close to a normal distribution, with a mean centered at this mean, we can think about how many standard deviations from the mean did he score in each of these situations. In both cases, he scored above the mean, but how many standard deviations above the mean?

So let's see if we can figure that out. For the LSAT, let me write this down. On the LSAT, he scored 172. So how many standard deviations is that going to be? Well, let's take 172, his score, minus the mean. So this is the absolute number that he scored above the mean, and now let's divide that by the standard deviation.

So on the LSAT, this is what this is going to be: 21 divided by 10. So this is 2.1 standard deviations above the mean. You could view this as a z-score; it's a z-score of 2.1. We are 2.1 above the mean in this situation.

Now let's think about how he did on the MCAT. On the MCAT, he scored a 37. The mean is a 25.1 and there is a standard deviation of 6.4. So let's see; 37.1 minus 25 would be 12, but now it's going to be 11.9.

11.9 divided by 6.4. So without even looking at this, this is going to be approximately, well, this is going to be a little bit less than 2. This is going to be less than 2.

So based on this information, we could figure out the exact number here. In fact, let me get my calculator out. So I get the calculator. If we do 11.9 divided by 6.4, that's going to get us to one point. I'll just say one point, I'll say approximately 1.86.

So approximately 1.86. So relatively speaking, he did slightly better on the LSAT. He did more standard deviations; although this is close, I would say they're comparable. He did roughly two standard deviations if we were to round to the nearest standard deviation.

But if you wanted to get precise, he did a little bit better relatively speaking on the LSAT. He did 2.1 standard deviations here, while over here he did 1.86 or 1.9 standard deviations. But in everyday language, you would probably say, well, this is comparable. If this was three standard deviations and this is one standard deviation, then you'd be like, oh, he definitely did better on the LSAT.

More Articles

View All
How the Kushites Took Over Egypt | Flooded Tombs of the Nile
[tense music] Nuri is one of the most intensive concentrations of pyramids anywhere in the world, across any culture and civilization. [upbeat music] In Sudan, in fact, there are more pyramids than in Egypt. And this is something that people don’t think …
15 Short Books With Huge Impact
We live in a world where time is often more precious than money or many other things. But what if you could experience the joy of reading without breaking a sweat or committing to a long and draining book? Welcome, Aluxer! Today we’re talking about 15 boo…
Solving square-root equations: no solution | Mathematics III | High School Math | Khan Academy
Let’s say that we have the radical equation: the square root of 3x minus seven plus the square root of 2x minus one is equal to zero. I encourage you to pause the video and see if you can solve for X before we work through it together. Alright, so one t…
Steve Varsano, founder of The Jet Business live on Bloomberg TV April 2013
Welcome back. You’re watching The Pulse. We’re live from Blue Books London headquarters. I’m Guy Johnson and I’m Francine Lacqua. Now, let’s get a perspective on the ECB and BOE’s upcoming policy decisions from a corporate executive. Stephen Varsano is f…
Misconceptions About the Universe
There was a time when the universe was expanding so rapidly that parts of it were moving apart from each other faster than the speed of light. That time is right now. A lot of people make a big deal out of the fact that during inflation, right after our u…
19-year-old dropout makes $60,000 per month online - Shopify Passive Income
Now but really quickly I want to say something to people that are watching. So okay, put this in perspective. Just think about this for a second. Nine months ago, less than a year ago, I was on my chair in my house on my computer watching this guy when he…