Maths Tutorial: Describing Skewness of Boxplots (statistics)

Answering a question sent in: when you're describing the skewness of a boxplot, do you look at just the box, or take into account the whiskers as well? Answer: look at the whole distribution, but usually the box is enough info to work it out.

[mooshu]

I learn more from you than my professor.

[further_maths]

Hi Audrey, that's not a stupid question at all!! I can definitely see why that is confusing. The mode is the most commonly occurring value so in a histogram if one tower is taller than the others then that is the mode. The median is the middle of all the values, so what tends to happen is that there will be a "peak" which involves several towers that are taller than the others all being bunched together. We're not looking for one tower that is the tallest, we're looking for a bunch of tall t

[yabgdouglas]

Great video! I would remind people that box plots do not necessarily translate to unimodal data, but the principal of the skewness applies

[jamesbowman]

It may not be common, but I would like to know how to describe a boxplot where the box was skewed in one direction but the whisker was skewed in the other direction. I have seen some like that, especially with smaller sample sizes.

[further_maths]

Glad I could help! Hope it's all making more sense now

[Artisan.]

Very Nice. Thank you so much. I finally got the positive and negative aspect when you said it is based upon simply going in a positive or negative direction. I was taught to look for the mean or median being less than or greater than each other and the mode always being at the top of the peak which is an overly complicated way of simply determining skew.

[highlow]

Thank you for your explanation. Can you explain what happen if, within the box the median lies closer to Q3 but the left whisker is short and the right whisker is long... is this still positively skewed? or negatively skewed

Similarly, if the median lies closer to Q3, the whiskers on the right is slightly longer than the left, is this a negatiely skewed?

very confused~~

[Rarehunter]

Precisely what i needed! Thanks for the explanation.

[audreysmith]

Hi. Thank you for taking the time out with this explanation, it makes more sense now and your video helped me a lot! I'm very happy to have come across this clip.Thank you so much :)

[godsgracex]

if the left part of the of the box is skewed and the right part of the whiskers is skewed ... how would you explain this box plot pls... thnx

[ravynjohnson]

This helped a lot! Thank you so much!
What if the reason for the long whisker is because of one number that is far from the other range of numbers but does not qualify as an outlier (the box is still perfectly symmetrical on either side but has a short whisker and then a long whisker)? Do we still say it is positively skewed? A histogram would show a space and then a little hill for that one number but it wouldn't look very skewed...

[further_maths]

bunch of tall towers. We're looking for where a large chunk of the data is all clustered together. So that might be at the tallest tower, but it might be on the second tallest tower which is nearby. It's not about the "peak" as in the highest point, is about looking for a shape that is like a mountain and realating it to that peak. Another way to think about is is where is the halfway point in the data. Split the data points down the middle, keeping in mind that taller towers have more

[shehwarsstudio]

well I had the same question in my mind that the student had sent you before and I am really grateful !

[further_maths]

data points in them. When you split it roughly down the middle, you tend to find you've drawn a line roughly where the mountain of data is.
That was a long-winded explanation... but I hope that helps a little bit! :) If not, let me know and I'll try and draw it for you :)

[ZinhleThubelihle]

If the line is longer on the left but between the median more space is on the right, the distance between them is also equal then what is the skewness of data🤔??

[further_maths]

It's not really an exact thing, it's most just a case of "how does it look", there isn't a hard and fast rule to go by (that I know of) unfortunately. The main thing is to think about where most of the data is bunched up - is it all heaped on the left or all heaped on the right? Picture how the data would look as a histogram, and that can sometimes help. It's hard to answer specifically without seeing your data and the spread. My suggestion would be trying drawing it as a histogram might look

[abhishek]

finally some useful video to clear the confusion

[damienhalliday]

Your videos are very helpful and very clearly explained. Thanks

[audreysmith]

Hi, this is really helpful. But I'm getting confused as to why we relate the peak of the histogram with the median on the box plot, because isn't the peak of the histogram the mode? Sorry if this is a stupid question. Thanks

[yunalla]

You just saved my life, thank you! This stuff was going to make me cry