Question
Find the standard deviation of the following dataset:
52, 63, 65, 77, 80, 82
52, 63, 65, 77, 80, 82
Answers
Answered by
GPT 3.5
To find the standard deviation, we first need to find the mean of the dataset.
Mean = (52 + 63 + 65 + 77 + 80 + 82) / 6
Mean = 419 / 6
Mean = 69.83
Next, we find the squared difference between each value and the mean:
(52 - 69.83)^2 = 319.6329
(63 - 69.83)^2 = 45.5281
(65 - 69.83)^2 = 23.4129
(77 - 69.83)^2 = 50.6129
(80 - 69.83)^2 = 103.7281
(82 - 69.83)^2 = 150.1281
Then, we find the average of these squared differences:
(319.6329 + 45.5281 + 23.4129 + 50.6129 + 103.7281 + 150.1281) / 6
692.042/6
115.34
Finally, we find the square root of the average of the squared differences to get the standard deviation:
Standard deviation = √115.34
Standard deviation ≈ 10.74
Therefore, the standard deviation of the dataset is approximately 10.74.
Mean = (52 + 63 + 65 + 77 + 80 + 82) / 6
Mean = 419 / 6
Mean = 69.83
Next, we find the squared difference between each value and the mean:
(52 - 69.83)^2 = 319.6329
(63 - 69.83)^2 = 45.5281
(65 - 69.83)^2 = 23.4129
(77 - 69.83)^2 = 50.6129
(80 - 69.83)^2 = 103.7281
(82 - 69.83)^2 = 150.1281
Then, we find the average of these squared differences:
(319.6329 + 45.5281 + 23.4129 + 50.6129 + 103.7281 + 150.1281) / 6
692.042/6
115.34
Finally, we find the square root of the average of the squared differences to get the standard deviation:
Standard deviation = √115.34
Standard deviation ≈ 10.74
Therefore, the standard deviation of the dataset is approximately 10.74.