Can we calculate the skewness of variables based on mean and median?

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The correct answer is FALSE.

Skewness is a measure of the asymmetry of a distribution. It is calculated by taking the third moment of a distribution about the mean, divided by the cube of the standard deviation. The mean and median are not sufficient to calculate skewness, because they do not provide information about the tails of the distribution.

To calculate skewness, we need to know the mean, median, and standard deviation of the distribution. The mean is the average of the values in the distribution. The median is the middle value in the distribution, when the values are arranged in order from least to greatest. The standard deviation is a measure of how spread out the values in the distribution are.

Once we have these three values, we can calculate the skewness using the following formula:

$$\text{Skewness} = \frac{\mu_3}{\sigma^3}$$

where $\mu_3$ is the third moment of the distribution about the mean and $\sigma$ is the standard deviation.

The skewness of a distribution can be positive, negative, or zero. A positive skew indicates that the distribution is skewed to the right, with a longer tail on the right side of the distribution. A negative skew indicates that the distribution is skewed to the left, with a longer tail on the left side of the distribution. A skewness of zero indicates that the distribution is symmetrical.

Skewness can be used to describe the shape of a distribution. It can also be used to identify outliers, which are values that are significantly different from the rest of the data.

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