replicate water samples were analyzed for water hardness with the following results : 102.2 , 102
.8 ,103.1, 102.3 of calcium trioxocarbonate . calculate the standard deviation of the mean and the coefficient of variation
And what is your problem with this. Can't you just substitute these numbers into the formula; i.e., plug and chug.
To calculate the standard deviation of the mean and the coefficient of variation, follow these steps:
Step 1: Calculate the mean (average) of the water hardness data.
Sum all the values of the water hardness measurements and divide it by the total number of measurements.
Mean = (102.2 + 102.8 + 103.1 + 102.3) / 4 = 410.4 / 4 = 102.6
Step 2: Calculate the squared difference between each value and the mean.
Subtract the mean from each value and square the result for every data point.
(102.2 - 102.6)^2 = 0.16
(102.8 - 102.6)^2 = 0.04
(103.1 - 102.6)^2 = 0.25
(102.3 - 102.6)^2 = 0.09
Step 3: Calculate the sum of the squared differences.
Add up all the squared differences calculated in Step 2.
Sum = 0.16 + 0.04 + 0.25 + 0.09 = 0.54
Step 4: Calculate the variance.
Divide the sum of squared differences from Step 3 by the total number of measurements minus one (n-1).
Variance = Sum / (n - 1) = 0.54 / (4 - 1) = 0.54 / 3 = 0.18
Step 5: Calculate the standard deviation.
Take the square root of the variance calculated in Step 4.
Standard Deviation = √(0.18) ≈ 0.424
Step 6: Calculate the coefficient of variation.
Divide the standard deviation (from Step 5) by the mean (from Step 1) and multiply by 100 to get the percentage.
Coefficient of Variation = (0.424 / 102.6) * 100 ≈ 0.413%
Therefore, the standard deviation of the mean is approximately 0.424 and the coefficient of variation is approximately 0.413%.