Question
Find the standard deviation of the following data set. 12, 14, 14, 15, 15, 15, 16, 19
Answers
Answered by
GPT 3.5
To find the standard deviation, we first need to calculate the mean of the data set:
(12 + 14 + 14 + 15 + 15 + 15 + 16 + 19) / 8 = 120 / 8 = 15
Next, we need to find the difference between each data point and the mean, square those differences, sum them up, divide by the number of data points, and take the square root:
(12 - 15)^2 = 9
(14 - 15)^2 = 1
(14 - 15)^2 = 1
(15 - 15)^2 = 0
(15 - 15)^2 = 0
(15 - 15)^2 = 0
(16 - 15)^2 = 1
(19 - 15)^2 = 16
(9 + 1 + 1 + 0 + 0 + 0 + 1 + 16) / 8 = 28 / 8 = 3.5
Taking the square root of 3.5 gives us the standard deviation:
√3.5 ≈ 1.87
Therefore, the standard deviation of the data set is approximately 1.87.
(12 + 14 + 14 + 15 + 15 + 15 + 16 + 19) / 8 = 120 / 8 = 15
Next, we need to find the difference between each data point and the mean, square those differences, sum them up, divide by the number of data points, and take the square root:
(12 - 15)^2 = 9
(14 - 15)^2 = 1
(14 - 15)^2 = 1
(15 - 15)^2 = 0
(15 - 15)^2 = 0
(15 - 15)^2 = 0
(16 - 15)^2 = 1
(19 - 15)^2 = 16
(9 + 1 + 1 + 0 + 0 + 0 + 1 + 16) / 8 = 28 / 8 = 3.5
Taking the square root of 3.5 gives us the standard deviation:
√3.5 ≈ 1.87
Therefore, the standard deviation of the data set is approximately 1.87.