Answer:
Option B
Explanation:
To find the standard deviation, we need to follow these steps:
1) Find the mean of the data set.
2) Calculate the difference between each data point and the mean.
3) Square each difference.
4) Find the average of the squared differences.
5) Take the square root of the average to get the standard deviation.
First, we find the mean of the data set:
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 46.4 / 6 = 7.73
Next, we calculate the difference between each data point and the mean:
| 7.2 - 7.73 | = 0.53
| 8.9 - 7.73 | = 1.17
| 2.7 - 7.73 | = 5.03
| 11.6 - 7.73 | = 3.87
| 5.8 - 7.73 | = 1.93
| 10.2 - 7.73 | = 2.47
Then, we square each difference:
0.53^2 = 0.2809
1.17^2 = 1.3689
5.03^2 = 25.3009
3.87^2 = 14.9569
1.93^2 = 3.7249
2.47^2 = 6.1009
Next, we find the average of the squared differences:
(0.2809 + 1.3689 + 25.3009 + 14.9569 + 3.7249 + 6.1009) / 6 = 8.62
Finally, we take the square root of the average to get the standard deviation:
sqrt(8.62) = 2.93
Therefore, the standard deviation of the data set is 2.93, which is option B.