18 Aug 2023

Posted on:

17 Aug 2023

0

# Resolved:Don't really understand what skewness means

You said in the positive skewed data the mean is bigger than median. Is it always so?

for example what if the dataset: 1, 2, 3, 4, 56, 57, 58

here the median is: 4

mean: 25.8

mode: 0

but in this dataset i provided the skewness according to the definition -skewness indicates whether the observations in a data set are concentrated on one side- isn't concentrated either on left or right side if we visualized it so there's no skewness -zero skew- and in the video mentioned when zero skew the mean = median unlike the dataset I provided!

So either I don't understand what does skewness mean or maybe not always when mean bigger than median so the data is positive skewed.

I really need some help to understand.

Instructor
Posted on:

18 Aug 2023

0

Hi Sayed,

Grea to hear from you.

Skewness is a measure of the asymmetry of a distribution. You're correct in your understanding that:

1) Positive skewness means the data is skewed to the right, with the tail of the distribution stretching further to the right, not the peak (the "hump" of the data set). In many cases of positive skewness, the mean is greater than the median.
2) Negative skewness means the data is skewed to the left, with the tail of the distribution stretching further to the left. Here, the mean is typically less than the median.
3) Zero skewness ideally implies that the data is perfectly symmetrical, and therefore the mean and median are the same.

However, the relationship between mean, median, and skewness is more of a general observation than a strict rule. While the mean being greater than the median often indicates positive skewness, there can be exceptions, especially for small datasets or datasets with peculiar characteristics.

In your dataset: 1, 2, 3, 4, 56, 57, 58, there's a clear gap between 4 and 56. This gap causes a "jump" in values. If you were to plot this dataset as a histogram or dot plot, you would observe two clusters of data points. The left cluster (from 1 to 4) and the right cluster (from 56 to 58).

Though the mean is greater than the median, this dataset isn't a classic example of a positively skewed dataset with a single, smooth tail stretching to the right. It's more of a bimodal distribution (two peaks) because of the two clusters. Hence, the typical relationship between mean, median, and skewness doesn't neatly apply here.

In summary, while the relationship between mean, median, and skewness can be a useful guideline to get a quick sense of the shape of a distribution, it's always a good idea to visualize the data to get a complete picture. There are also statistical measures of skewness that can be computed to get a more quantitative sense of the distribution's shape.

Best,
Ned