How is skew defined in your textbook? Range, standard deviation, and mean are pretty well-known terms, but skew is not so well known.Mr Davis 97 said:
The measure of skewness indicates the asymmetry in a distribution. Positive skewness means that the tail of the distribution is longer on the right side, while negative skewness means that the tail is longer on the left side. This can affect the standard deviation because extreme values on one side of the distribution can pull the mean in that direction, resulting in a larger standard deviation.
Yes, a distribution with a large range can have a low standard deviation if the data points are close to each other and the majority of the data is clustered around the mean. However, if the data points are spread out, the standard deviation will also be large.
The range is the difference between the highest and lowest values in a dataset. A larger range indicates more variability in the data, which can result in a larger standard deviation. This is because the standard deviation is a measure of how much the data points deviate from the mean, and a larger range means there is more variation from the mean.
Yes, outliers can significantly affect the standard deviation. Outliers are data points that are significantly different from the rest of the data, and they can pull the mean in their direction, resulting in a larger standard deviation. Therefore, it is important to identify and handle outliers appropriately in data analysis.
No, the standard deviation cannot be negative. It is a measure of dispersion, and it represents the average distance of the data points from the mean. Therefore, it is always a positive value or zero if all the data points are the same.
