Answer:
The best measure of central tendency to use in a set of data depends on the characteristics of the data and the specific objective of the analysis. Let's examine the given data set: 12, 8, 15, 45, 7, 13.
Mean: The mean, also known as the average, is calculated by summing up all the values in the data set and dividing by the total number of values. The mean is sensitive to extreme values and can be influenced by outliers. In this case, the mean is calculated as (12 + 8 + 15 + 45 + 7 + 13) / 6 = 100 / 6 ≈ 16.67.
Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. The median is not affected by extreme values and is a good measure to use when there are outliers or when the data is not symmetrically distributed. In this case, when the data set is arranged in ascending order, the median is 13, as it is the middle value.
Mode: The mode is the value that appears most frequently in a data set. It is a useful measure when we want to identify the most common value in the data set. In this case, the mode is not applicable as there are no repeated values in the data set.
Based on the characteristics of the given data set, the median is a good measure to use as it is not affected by extreme values and provides a central value that represents the middle of the data set. The mean may be influenced by the outlier value of 45, and the mode is not applicable in this case. So, the best measure of central tendency to use in this data set would be the median.