What significance does variance have to a set of data?

is variance the same as coefficent of variation?

when using coefficient of skewness, if you have a +1 or -1 value it signifies a high degree of skew. So does that refer to a postive/ negative skew or if not what exactly does it mean?

Thanks

Variance is a measure of how spread out the data points are in a data set. It quantifies the average squared deviation of each data point from the mean. In other words, it provides information about the variability and dispersion of the data. A larger variance indicates that the data points are more spread out, while a smaller variance suggests that the data points are closer together.

The coefficient of variation (CV), on the other hand, is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean. It is often expressed as a percentage. The coefficient of variation is used to compare the variability of different data sets, taking into account the scale of the data. It allows for comparing the relative dispersion of data sets with different means.

In terms of coefficient of skewness, a value of +1 or -1 does not necessarily signify a high degree of skew. The coefficient of skewness measures the asymmetry of the distribution. A positive value indicates a right-skewed distribution, where the tail of the distribution is stretched towards the right, while a negative value indicates a left-skewed distribution, where the tail is stretched towards the left. The magnitude of the coefficient of skewness indicates the degree of skewness; the closer the absolute value to zero, the less skewed the distribution is. A coefficient of skewness with an absolute value of 1 would generally be considered moderately skewed, but the interpretation may depend on the context and the specific data set.

To calculate the variance, you can follow these steps:
1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Calculate the average of the squared differences obtained from step 2.

To calculate the coefficient of variation, follow these steps:
1. Calculate the standard deviation of the data set.
2. Divide the standard deviation by the mean.
3. Multiply the result by 100 to express it as a percentage.

To calculate the coefficient of skewness, follow these steps:
1. Calculate the mean and standard deviation of the data set.
2. For each data point, subtract the mean and divide by the standard deviation.
3. Sum the cube of these standardized values.
4. Multiply the result by 1/(n * standard deviation^3), where n is the number of data points.
5. The resulting value is the coefficient of skewness.