To determine which year the mean is the best measure of central tendency, we need to look at both the mean and the standard deviation for each year. A lower standard deviation indicates that the data points are closer to the mean, meaning the mean is a more reliable measure of central tendency.
The results for each year are given as follows:
- 2005: Mean = 29.6, Standard Deviation = 9.93176721434811
- 2006: Mean = 7.6, Standard Deviation = 2.727636339397171
- 2007: Mean = 15.0, Standard Deviation = 7.0710678118654755
- 2008: Mean = 37.0, Standard Deviation = 14.805404418657398
Now let's interpret these results:
1. 2005:
- Mean = 29.6
- Standard Deviation = 9.93176721434811
2. 2006:
- Mean = 7.6
- Standard Deviation = 2.727636339397171
3. 2007:
- Mean = 15.0
- Standard Deviation = 7.0710678118654755
4. 2008:
- Mean = 37.0
- Standard Deviation = 14.805404418657398
The standard deviation is lowest for the year 2006 with a value of 2.727636339397171. This suggests that in 2006, the data points are closest to the mean compared to other years, making the mean the best measure of central tendency for this year.
Therefore, the correct choice is:
B) 2006
