Find the measures of center. What value best represents all the measures of center for the following data set?
12, 13, 40, 95, 88, 7, 95
There are three commonly used measures of center:
1. Mean - the sum of all the values divided by the number of values:
(12 + 13 + 40 + 95 + 88 + 7 + 95) / 7 = 50
2. Median - the middle value when the data set is arranged in order:
7, 12, 13, 40, 88, 95, 95
The median is 40.
3. Mode - the most frequently occurring value in the data set:
There are two values that occur twice, 95 and 7.
None of these measures of center is necessarily "best" - it depends on the context and the specific question being asked. In this case, all three measures give different information about the data set. The mean may be affected by outliers (in this case, the two high values of 95), while the median and mode are more robust to extreme values. Ultimately, the choice of measure should be based on the purpose of the analysis and the characteristics of the data set.