I have been trying to solve this problem for over half an hour now. I don't know if it is to do with my incapability of using a calculator or a misunderstanding in standard deviation.
Question:
A sample of 10 people complete a task and their times, x, are recorded. Given that Σx = 273 and Σx²=7561, calculate the mean and standard deviation of the times taken.
Attempt of a solution:
The mean would be Σx / n. Therefore, the mean is 273/10 = 27.3
As for standard deviation, since it is a sample, we would use the formula: Link to the formula
But when I type √(7561/(10-1))-27.3² (square root over whole thing) , I get 9.74 (3sf)
Actual Answer:
= 3.29 (EDIT: The answer on the book was incorrect?)
Best Answer
sample standard deviation $= \sqrt{\left(\dfrac{\sum (x-\bar x)^2}{n-1}\right)}$$= \sqrt{\left(\dfrac{\sum x^2 - 2\bar x \sum X + n\bar x ^2}{9}\right)}$
$=\sqrt{\left(\dfrac{\sum x^2 - \frac{(\sum X)^2}{n}}{9}\right)}$
$ = \sqrt{\left(\dfrac{7561 - \frac{273^2}{10}}{9}\right)} = \sqrt{12.0111} = 3.47$