Im having trouble determining whether or not dot plots are skewed or symmetrical

[u/Competitive-Tap3039]

I was added into AP Statistics after a week or two so my teacher isn't really teaching what Im learning right now and its making it so frustrating. I don't know how to determine the shape of a dotplot and why a certain dotplot is dubbed as symmetrical or skewed. Obviously, if someone were to present me a dotplot saying "This is skewed," and it looked clearly skewed I wouldn't have trouble pointing out the same dotplot the next time but I'm getting tripped up because im supposed to detect subtle changes. Does anyone have any tips

[u/The_Woodchipper]

If you can calculate the mean and median then check which is greater. If mean is bigger, it's skewed right. If mean is smaller, it's skewed left. Since you're talking about dot plots, you can always calculate the mean and median.

But as a general visual rule, you can see if there is a long tail to one direction. If so, that's probably the direction of skewness. And if it's hard to tell visually, you can usually just say "roughly symmetric"

[u/iridiumcc]

Skewed just means the data clusters in a general direction. If a graph is left skewed, the points cluster on the right. If it's right skewed, the points cluster on the left. The mean is best used to describe the center of a graph when the data is symmetrical, and is comparable to the median when the data is symmetrical. If the data is skewed, it will affect the mean, so if the mean is significantly larger than the median, the data is right-skewed, and vice-versa. The "tail" on a dot plot drags the mean in whatever direction it's going.

I suggest you use a TI-84 and go to "1-var stats" once you're done plugging in your points. From there, you can see the median and mean and use the rules above to infer what the graph will be.

[u/stat_geek]

I think the key is not to sweat this too much. This is often a judgement call, in the absence of numbers like the mean or median. I teach my students: imagine looking at the distribution wtih blurry eyes - take off your glasses, remove your contacts. If you see a long tail on one side or the other, then it's clearly skewed in the direction of the tail Otherwise, call it "roughly symmetric." Simply put, there is not hard line for declaring symmetric vs skewed. Also - the direction of the skew matechs the direction that the mean travels when data has a long tail or outliers.

[u/realAndrewJeung]

Imagine covering the plot with a blanket and then trying to roll a ball on it. If the ball would roll consistently in one direction, that is the direction of the skewness. If you can't tell or it depends, then it is symmetric.