Two data sets are being compared. One data set is skewed left, and the minimum value is an outlier. Another data set is symmetric about its peak about the center of the distribution with no outliers. Explain whether the mean and standard deviation should be used to compare the measures of center and measures of spread.(1 point)
Responses
The mean and the standard deviation should be used because one of the distributions is symmetric with no outliers.
The mean and standard deviation should not be used because both of the distributions are skewed left, and both data sets have at least one outlier.
The mean and standard deviation should not be used because one of the distributions is skewed left and has an outlier.
The mean and the standard deviation should be used because the mean and the standard deviation are not affected by outliers.
The mean and the standard deviation should not be used because one of the distributions is skewed left and has an outlier. Outliers can greatly affect the mean and standard deviation, making them not good measures of center and spread when dealing with skewed distributions and outliers. In this case, using the median and interquartile range or other robust measures would be more appropriate for comparing the two data sets.
What is the answer the first, second, third, or fourth answer
The answer is: the third answer - The mean and standard deviation should not be used because one of the distributions is skewed left and has an outlier.
The correct response is: The mean and the standard deviation should not be used because one of the distributions is skewed left and has an outlier.
To explain why, we need to understand what the mean and the standard deviation represent. The mean is a measure of central tendency, or the average value of a dataset. The standard deviation is a measure of spread, or how the data is dispersed around the mean.
In this case, one of the datasets is skewed left, which means that it has a longer tail on the left side and the majority of the data points are on the right side. Skewness can affect the mean by pulling it in the direction of the longer tail. In this situation, the mean may not accurately represent the typical value of the dataset.
Additionally, one of the datasets has an outlier, which is a data point that is significantly different from the other values. Outliers can have a large impact on the mean since they can either be much larger or much smaller than the other values. This means that the mean may not be a reliable measure of central tendency when outliers are present.
The standard deviation is also influenced by outliers since it takes into account the variability of all the data points. Outliers can increase the standard deviation, making it an unreliable measure of spread.
Therefore, in this scenario, it is not appropriate to use the mean and the standard deviation to compare the measures of center and measures of spread between the two datasets.