What is a SYMMETRIC versus SKEWED DISTRIBUTION, give an example?

Expert Solution

Distribution of data can be symmetrical or skewed, depending upon the nature of the data. A data distribution is symmetrical when its mean and median is equal to each other. Besides, in a unimodal distribution, the mean, median and mode will be same and equal to be symmetrical. But, in in skewed data distribution, the mean and mode will not be equal. A skewed data distribution, there can be positively skewed (having skewed to the right) and negatively skewed (having skewed to the left) distribution. When distribution is positively skewed, then mean is greater than median and median is greater than mode. If distribution is negatively skewed, then mean will be lower than the median and median is lower than mode. Besides, symmetric distribution forms the mirror image if divided into two halves, but it is not the case with skewed distribution. It can be understood by the following distributions.

The first distribution is 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 10. It is symmetrical distribution. Here, mean and median is 7.

The second distribution is 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8. It is negatively skewed. Here, mean is 6.45 and median is 7.

The third distribution is 6, 6, 7, 7, 7, 7, 8, 9, 10. It is positively skewed. Here, the mean is 7.44 and median is 7.

Graphical representations are as follows:

keosha answered 1 year ago

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