Find the mean and standard deviation of the following data set. Round to the nearest tenth. 11,14,15,16,16,17,18,19,23
Mean: (11+14+15+16+16+17+18+19+23) / 9 = 149 / 9 = 16.6 (rounded to the nearest tenth)
To find the standard deviation, first calculate the variance:
1. Find the mean of the data set: 16.6
2. Subtract the mean from each number in the data set, then square the result:
(11-16.6)^2 = 31.36
(14-16.6)^2 = 6.76
(15-16.6)^2 = 2.56
(16-16.6)^2 = 0.36
(16-16.6)^2 = 0.36
(17-16.6)^2 = 0.16
(18-16.6)^2 = 2.56
(19-16.6)^2 = 5.76
(23-16.6)^2 = 40.96
3. Find the sum of the squared differences: 31.36 + 6.76 + 2.56 + 0.36 + 0.36 + 0.16 + 2.56 + 5.76 + 40.96 = 90.84
4. Divide the sum by n-1 (where n is the number of data points): 90.84 / 8 = 11.355
5. Find the square root of the variance to get the standard deviation: sqrt(11.355) = 3.4 (rounded to the nearest tenth)
Therefore, the standard deviation of the data set is 3.4 (rounded to the nearest tenth).