Problema Solution
A certain company recorded the number of employee absences each week over a period of 10 weeks. The result is the data list 6, 5, 1, 2, 2, 4, 7, 4, 5, 5. Find the mean and standard deviation of the number of absences per week. Round the standard deviation to two decimal places.
mean days
standard deviation days
Answer provided by our tutors
mean = the simple average of the numbers 6, 5, 1, 2, 2, 4, 7, 4, 5, 5
(6 + 5 + 1 + 2 + 2 + 4 + 7 + 4 + 5 + 5)/9 = 41/9
the steps for calculation standard deviation are:
1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result
3. Then work out the mean of those squared differences.
4. Take the square root of that and we have the standard deviation
1. we already did 1. that is we know the mean is 41/9
2. and 3.
[(6 - 41/9)^2 + (5- 41/9)^2 + (1- 41/9)^2 + (2- 41/9)^2 + (2- 41/9)^2 + (4- 41/9)^2 + (7- 41/9)^2 + (4- 41/9)^2 + (5- 41/9)^2 + (5- 41/9)^2]/9 = 34.9753086/9 = 3.8861454
click here to see the calculation:
4. standard deviation = sq. root of 3.8861454
standard deviation = 1.9713