A data set has a mean of 14.5 and a median of 11.2. Which of the following terms would describe this data set?
A data set with a mean of 14.5 and a median of 11.2 is skewed right.
In a data set, when the mean is greater than the median, it typically indicates that the distribution is skewed to the right, meaning that there are outliers or a tail on the higher end of the data. This discrepancy suggests that higher values are pulling the mean up more than the median.
A bimodal distribution is characterized by having two modes, or peaks, in its frequency distribution. The information provided only mentions the mean and median, which do not indicate the presence of multiple peaks. Therefore, without further data showing two distinct modes, this choice does not accurately describe the data set.
A left-skewed distribution occurs when the mean is less than the median, indicating that there are outliers or a tail on the lower end of the data. Since the mean (14.5) is greater than the median (11.2) in this data set, it cannot be described as skewed left.
A symmetrical distribution has equal mean and median values, indicating a balanced spread of data around a central point. In this case, the mean and median are not equal (mean = 14.5 and median = 11.2), thus the data set cannot be categorized as symmetrical.
The data set in question, with a mean of 14.5 and a median of 11.2, reflects a right-skewed distribution where higher values influence the mean more significantly than the median. This skewness indicates that the bulk of the data values are concentrated on the lower end, with a few high outliers extending the mean. Understanding these characteristics is essential for interpreting data distributions accurately.
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