Final answer:
The median is the best measure to describe the center of the data set (3,7,4,2,31,5,4) due to an outlier present in the data, which skews the mean.
Step-by-step explanation:
In a given data set such as (3,7,4,2,31,5,4), the measure that best describes the set of data depends on the characteristics of the data. Given that the number 31 is significantly higher than the rest and could be considered an outlier, the median would likely be the best measure to represent the center of this data set. The median is the middle value when the data is ordered, which reduces the impact of outliers.
To find the median, first order the data: (2, 3, 4, 4, 5, 7, 31). Since there are seven data values, the median is the fourth value, which is 4. Had there been an even number of data points, the median would have been the average of the two middle values.
The mean would be skewed due to the outlier (31), and the mode could potentially be 4, the most frequently occurring value. In this case, since the mean is greatly affected by the outlier and there is no particularly informative mode, the median is the measure that most accurately describes the central tendency of the data set.