For the set of data 0.752, 0.756, 0.752, 0.751, and 0.760 ppm Pb . calculate the coefficient of variation.
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1 point
0.50%
0.05 %
non of all
0.0038 %
To calculate the coefficient of variation, we first need to find the mean and standard deviation of the data set.
Mean (μ) = (0.752 + 0.756 + 0.752 + 0.751 + 0.760) / 5 = 3.771 / 5 = 0.7542
Next, calculate the standard deviation (σ):
1. Calculate the squared differences between each data point and the mean:
(0.752 - 0.7542)^2 = 0.000048
(0.756 - 0.7542)^2 = 0.000032
(0.752 - 0.7542)^2 = 0.000048
(0.751 - 0.7542)^2 = 0.000102
(0.760 - 0.7542)^2 = 0.003364
2. Calculate the variance:
(0.000048 + 0.000032 + 0.000048 + 0.000102 + 0.003364) / 4 = 0.0001264
3. Take the square root of the variance to get the standard deviation:
sqrt(0.0001264) ≈ 0.0112347
Now, calculate the coefficient of variation:
Coefficient of Variation = (standard deviation / mean) * 100
Coefficient of Variation = (0.0112347 / 0.7542) * 100 ≈ 1.49%
Therefore, the coefficient of variation for the given data set is 1.49%. None of the options provided match this value.