skew value is negative but while plotting it shows positive.

**

Length
8.312
8.343
8.317
8.383
8.348
8.410
8.351
8.373
8.481
8.422
8.476
8.382
8.484
8.403
8.414
8.419
8.385
8.465
8.498
8.447
8.436
8.413
8.489
8.414
8.481
8.415
8.479
8.429
8.458
8.462
8.460
8.444
8.429
8.460
8.412
8.420
8.410
8.405
8.323
8.420
8.396
8.447
8.405
8.439
8.411
8.427
8.420
8.498
8.409
**
#c <- screwlength$Length
Version:1.0 StartHTML:0000000107 EndHTML:0000000921 StartFragment:0000000127 EndFragment:0000000903

#boxplot(c)
#skewness(c)
-0.4706845

#plot(density(c))

I was using skew function with above data. I am getting the negative skew value but while plotting it is opposite. For eg. I got the result from summary() i.e. mean>median but skewed value is negative (so it should be like median >mean). Can somebody try to explain me, where is the problem or am I doing something wrong? Thankyou in advance.

You can tune a data set to have the mean just above the median yet still have negative skew.

> X <- c(8.30, rep(8.4, 5), 8.41, 8.42, 8.49)
> X
[1] 8.30 8.40 8.40 8.40 8.40 8.40 8.41 8.42 8.49
> median(X)
[1] 8.4
> mean(X)
[1] 8.402222
> e1071::skewness(X)
[1] -0.3837484

I think judging skew from the shape of a histogram is hard to do accurately, so I do not put much weight on that.

For a unimodal distribution, negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule.

Skewness - Wikipedia

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