a sample of the personal files of eight male employees revealed that during a six month period they lost the following number of days due to illness 2, 0, 6, 3, 10, 4, 1, 2 calculate the standard deviation show your work
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.
To calculate the standard deviation, you will need to follow these steps:
Step 1: Calculate the mean (average)
Step 2: Calculate the variance
Step 3: Calculate the standard deviation
Step 1: Calculate the mean
The mean is calculated by summing up all the values in the dataset and dividing it by the total number of values. In this case, there are 8 values:
2 + 0 + 6 + 3 + 10 + 4 + 1 + 2 = 28
Mean = 28 / 8 = 3.5
The mean of the dataset is 3.5.
Step 2: Calculate the variance
The variance represents the average of the squared deviation of each value from the mean. To calculate the variance, follow these steps:
a) Subtract the mean from each data point.
b) Square the result of each subtraction.
c) Sum up all the squared values.
d) Divide the sum by the total number of values.
Let's calculate the variance for each value:
(2 - 3.5)^2 = 2.25
(0 - 3.5)^2 = 12.25
(6 - 3.5)^2 = 6.25
(3 - 3.5)^2 = 0.25
(10 - 3.5)^2 = 40.25
(4 - 3.5)^2 = 0.25
(1 - 3.5)^2 = 6.25
(2 - 3.5)^2 = 2.25
Sum of squared differences = 70.75
Variance = 70.75 / 8 = 8.84
The variance of the dataset is 8.84.
Step 3: Calculate the standard deviation
The standard deviation is the square root of the variance. To calculate the standard deviation, take the square root of the variance:
Standard Deviation = √(8.84) = 2.97 (rounded to two decimal places)
The standard deviation of the dataset is approximately 2.97.