Major Questions in Statistics - Essay Example

If the data is significantly skewed, the mean becomes an inappropriate measure of central tendency. It should be noted that the mean will be more likely to be found on the dataset where the skewness can be found. For example, a data set that ranges from 7-40 which is positively skewed can have a mean which is 15 only because most of the data range from 7-18 for instance. The presence of outliers that are extremely low or high data can also adversely affect the effectiveness of the mean as a measure of central tendency.

If data is significantly skewed, the mode becomes the best approximation of the data’s center. The Mean cannot be relied upon because of the presence of outliers while the median can also be misleading. Thus, a mode that represents the most number of variables can best represent the data center in this situation.

If the data is significantly skewed, the range will not be affected. It should be noted that as the range is only a measure of the dispersion of data, it does not indicate how the data looks like. The range is simply a measurement of the values within the data set. However, it should also be noted that the presence of outliers in the data set will make the range very high.

Asymmetrical data is expected to have a skewness of 0 because the standard deviation is zero. Thus, when the standard deviation of a data set is computed as zero, it follows that it is normally distributed.

The interquartile range is affected by the dispersion of the data set. It should be noted that as it looks at 50% of the data set, the gap between the 3rd and the 1st quartile cannot fully indicate the dispersion because of the presence of observations that are in the lowest or highest quartiles. However, it is effective in removing the possibility of being misled by the presence of outliers.

f the data is significantly skewed, the interquartile range serves as the best measure of dispersion. It should be noted that the interquartile range measures the dispersion by looking at 50% of the observation. It removes the possibility of having misleading measures of central tendency by capturing the middle of the data and leaving the outliers behind. This is in contrast with a range that is very sensitive to the presence of outliers. Standard deviation on the other hand is very much dependent on the mean and as stated above, the mean becomes an inappropriate measure of central tendency if the data set is significantly skewed.

In the computation presented above, the D1 has the skewness which is closest to zero though none of the variables considered has a skewness of zero. This finding indicates that none of the variables above will have a perfect bell-shaped data set when graphed. However, we would expect that D1 is close to perfection but is a little positively skewed.