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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: PopcornTime on December 13, 2017, 10:36:05 am

Title: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: PopcornTime on December 13, 2017, 10:36:05 am

Sorry for all the questions, but is it possible to mathematically calculate whether a distribution is positively/negatively skewed. Kind of like calculating whether or not a value is an outlier?

Only because there are some box plots and histograms on VCAA exams which are kind of dodgy and its hard to work out whether they are approximately symmetric or positively/negatively.

Thanks

Title: Re: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: AngelWings on December 13, 2017, 03:10:15 pm

Majority of the time in Further, positively and negative skewed distributions are done qualitatively and just 'by eye'. There's a slightly mathematical way by identifying the mean and median's relative locations with each other.

General Rule
Positively skewed: mean > median
Symmetrical: mean = median
Negatively skewed: mean < median
(This works most of the time.)

Title: Re: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: mtDNA on December 13, 2017, 04:58:56 pm

Quote from: PopcornTime on December 13, 2017, 10:36:05 am

Sorry for all the questions, but is it possible to mathematically calculate whether a distribution is positively/negatively skewed. Kind of like calculating whether or not a value is an outlier?

Only because there are some box plots and histograms on VCAA exams which are kind of dodgy and its hard to work out whether they are approximately symmetric or positively/negatively.

Thanks

Although it may seem dodgy now, all I can suggest is to do practise - after a while, you’ll be able to do it confidently (and extremely quickly) by eye!

Title: Re: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: MissSmiley on January 05, 2018, 06:51:41 pm

Quote from: PopcornTime on December 13, 2017, 10:36:05 am

is it possible to mathematically calculate whether a distribution is positively/negatively skewed. Kind of like calculating whether or not a value is an outlier?

Hi!
This is a really handy visual summary picture that I used, and it can just go right into your summary book! :)
Although it's not the mathematical way for finding out the positive or negative skew, you can relate the question distribution visually to this sheet!
(plus it's also got dot plot and stem and leaf plot distributions and frequency polygons along with the histogram!) :)
Hope this helps! :)

Title: Re: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: Sine on January 06, 2018, 12:04:38 am

I always thought of it by looking at the tail end which is really the "outlier's" although not mathematically outliers.
If the tail is in the negative we have negative "outliers" hence a negative "skew"
same can be done for positive skew.

Title: Re: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: kiwikoala on January 06, 2018, 01:05:11 am

Quote from: AngelWings on December 13, 2017, 03:10:15 pm

General Rule
Positively skewed: mean > median
Symmetrical: mean = median
Negatively skewed: mean < median
(This works most of the time.)

Here's the photo
(https://qph.ec.quoracdn.net/main-qimg-a1e0adc0e991e6af793242f824112189-c)

Title: Re: Is there a way to find whether a distribution is positively/ negatively skewed?
Post by: spectroscopy on January 06, 2018, 02:38:24 am

for further maths the above stated information is definitely sufficient. There are calculations that you can do to calculate skewness numerically and get a value for a data set's skew but this is well beyond the requirements for vce further maths, but it is something you will learn in the first week of university statistics