Final answer:
To compare the distributions, use mean and standard deviation for symmetric distributions, and median and IQR for skewed distributions, alongside graphical representations like box plots or histograms.
Step-by-step explanation:
Comparing Distributions Using Statistical Measures
To compare the distributions of data sets, you must consider the shape of the data. If the distributions are symmetric, you can compare them using the mean and standard deviation. The mean provides a measure of the central tendency, and the standard deviation gives you an idea of the spread of the data around the mean. However, when the data is skewed, the mean and standard deviation may not provide an accurate picture of the data, since they can be influenced by outliers.
In the case of skewed distributions, it is more informative to use the median, which is less affected by outliers, and the interquartile range (IQR), which measures the middle 50 percent of the data. The IQR is especially useful for identifying outliers, which can be determined using the IQR method (1.5×IQR above the third quartile or below the first quartile). Understanding the spread of the middle portion of the data helps to provide a comparison that is more resistant to skewness or outliers.
Therefore, for skewed distributions, it is recommended to use the first quartile, median, third quartile, and IQR, alongside a graphical representation such as a box plot or histogram, to gain a more comprehensive understanding of the data.