Questions: Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set? 29,30,31,30,30,34,32,28 Select the correct answer below: Mean Median

Solution Steps

To determine whether the mean or the median is a better measure of the center of the data set, we should consider the presence of outliers or skewness in the data. The mean is sensitive to outliers, while the median is more robust. Calculate both the mean and the median, and compare them to see if there is a significant difference, which might suggest the presence of outliers.

The mean of a data set is calculated by summing all the values and dividing by the number of values. For the data set \([29, 30, 31, 30, 30, 34, 32, 28]\), the mean is:

\[ \text{Mean} = \frac{29 + 30 + 31 + 30 + 30 + 34 + 32 + 28}{8} = \frac{244}{8} = 30.5 \]

To find the median, first arrange the data in ascending order: \([28, 29, 30, 30, 30, 31, 32, 34]\). Since there are 8 values (an even number), the median is the average of the 4th and 5th values:

\[ \text{Median} = \frac{30 + 30}{2} = 30.0 \]

The mean is \(30.5\) and the median is \(30.0\). The mean is slightly higher than the median, which suggests that there might be a slight skew in the data. However, the difference is not substantial, indicating that there are no significant outliers affecting the mean.

Final Answer