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### Course: Integrated math 1>Unit 10

Lesson 1: Displays of distributions

# Shapes of distributions

Some distributions are symmetrical, with data evenly distributed about the mean. Other distributions are "skewed," with data tending to the left or right of the mean. We sometimes say that skewed distributions have "tails.".

## Want to join the conversation?

• So I'm a bit confused. We say skewed to the left, that means that means that most of the data is towards the left or the right?
• This was really bothering me, too, Jono, and I really appreciated your question. I was just about to post the same thing myself when I saw your post. Then today I was watching Sal's video on comparing distribution means. At around in the video, Sal is talking about an outlier, and he mentions that it skews the data, it drags the mean upward. Then it suddenly all made sense. The data in the tail is off centered from the normal distribution, and it is literally skewing the mean in that direction. Anyway, it made a lot more sense to me when I saw that.

Here's the url for the video in case anyone wants to see it:

• my favorite part was when he burped
• how does this look like an armadillo? looks more like a slug.
• if the mean and median in a data set are the same, can we just conclude that the data is symmetrical?
• I think I can come up with a counterexample.
3 4 5 5 8. The mean and median are both 5, but they do not appear symmetrical.
• if it is approximately symmetrical, wouldn't it be left-tailed and right-tailed?
• If you think of it like a pyramid the very top will be symmetrical. IF you have both a right and left tail. I know its confusing.
• What does Sal mean when he says if it’s leftailed it’s PROBABLY left skewed, how do we know for sure?
• When Sal mentions that if it's left-tailed, it's probably left-skewed, he's highlighting a general tendency. Left-tailed distributions often have more values on the lower end, making them left-skewed. However, it's not a strict rule, and other factors can influence skewness. Skewness is a more precise statistical measure, but for practical purposes, you can often infer skewness from the direction of the tail in a distribution.
• What is approximately symmetrical mean?
• Almost, but not completely symmetrical.

An approximately symmetrical distribution is a distribution that isn't very clearly left- or right-tailed.
• Is it the opposite so if i am looking on my left would that be their right?🤨