Final answer:
The mean for the set of data is 19 and the standard deviation is approximately 8.21.
Step-by-step explanation:
The mean of a set of data is the average value, which can be calculated by summing all the data points and dividing by the number of data points. In this case, the sum of the data points is 31 + 12 + 21 + 6 + 28 + 5 + 26 + 23 + 19 = 171. Dividing that by 9 (the number of data points) gives a mean of 19.
The standard deviation measures how spread out the data points are from the mean. It is calculated by finding the square root of the variance. To find the standard deviation for this set of data, we need to first calculate the variance:
1. Find the mean of the data set:
(31 + 12 + 21 + 6 + 28 + 5 + 26 + 23 + 19) / 9 = 171 / 9 = 19
2. Find the deviation from the mean for each data point:
31 - 19 = 12
12 - 19 = -7
21 - 19 = 2
3. Square each deviation:
12^2 = 144
(-7)^2 = 49
2^2 = 4
4. Find the mean of the squared deviations:
(144 + 49 + 4 + 169 + 9 + 196 + 16 + 16 + 4) / 9 = 607 / 9 = 67.44
5. Find the square root of the variance:
sqrt(67.44) = 8.21
Therefore, the standard deviation for this set of data is approximately 8.21.