A quality control manager at a poultry farm is monitoring the weight of eggs produced. The weights of 20 randomly selected eggs (in grams) are as follows: 65, 68, 60, 76, 65, 74, 58, 56, 61, 57, 63, 64, 72, 66, 65, 67, 65, 63, 67, 67. Find the coefficient of variation.

To find the coefficient of variation, we first need to calculate the mean (average) and the standard deviation of the data set.

Step 1: Calculate the mean Add up all the weights and divide by the number of weights.

65 + 68 + 60 + 76 + 65 + 74 + 58 + 56 + 61 + 57 + 63 + 64 + 72 + 66 + 65 + 67 + 65 + 63 + 67 + 67 = 1320

1320 / 20 = 66 (This is the mean)

Step 2: Calculate the standard deviation First, subtract the mean from each weight to get the deviation of each weight. Then square each deviation. Add up all these squared deviations. Divide that sum by the number of weights minus 1 (this is called the "degrees of freedom"). Finally, take the square root of that quotient.

The squared deviations are: (65-66)^2 = 1, (68-66)^2 = 4, (60-66)^2 = 36, (76-66)^2 = 100, (65-66)^2 = 1, (74-66)^2 = 64, (58-66)^2 = 64, (56-66)^2 = 100, (61-66)^2 = 25, (57-66)^2 = 81, (63-66)^2 = 9, (64-66)^2 = 4, (72-66)^2 = 36, (66-66)^2 = 0, (65-66)^2 = 1, (67-66)^2 = 1, (65-66)^2 = 1, (63-66)^2 = 9, (67-66)^2 = 1, (67-66)^2 = 1

The sum of these squared deviations is 528.

528 / (20-1) = 27.79 (This is the variance)

The square root of the variance is the standard deviation, so √27.79 = 5.27 (This is the standard deviation)

Step 3: Calculate the coefficient of variation The coefficient of variation is the standard deviation divided by the mean, multiplied by 100% to turn it into a percentage.

(5.27 / 66) * 100% = 7.98%

So, the coefficient of variation of the egg weights is approximately 7.98%.