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To find the standard deviation of the masses of chicken eggs, we will follow these steps:

### Step 1: Calculate each \((x - \mu)\) term
The mean mass \(\mu\) is given as 71.2, and we have five values of \(x\):
- \(x_1 = 67\)
- \(x_2 = 74\)
- \(x_3 = 68\)
- \(x_4 = 75\)
- \(x_5 = 72\)

Calculate \((x - \mu)\) for each value of \(x\):
1. \(67 - 71.2 = -4.2\)
2. \(74 - 71.2 = 2.8\)
3. \(68 - 71.2 = -3.2\)
4. \(75 - 71.2 = 3.8\)
5. \(72 - 71.2 = 0.8\)

### Step 2: Calculate each \((x - \mu)^2\) term
Square each result from Step 1:
1. \((-4.2)^2 = 17.64\)
2. \((2.8)^2 = 7.84\)
3. \((-3.2)^2 = 10.24\)
4. \((3.8)^2 = 14.44\)
5. \((0.8)^2 = 0.64\)

### Step 3: Calculate the variance
The variance is the average of these squared deviations, calculated as:
\[
\text{Variance} = \frac{\sum (x - \mu)^2}{n} = \frac{17.64 + 7.84 + 10.24 + 14.44 + 0.64}{5}
\]
\[
= \frac{50.8}{5} = 10.16
\]

### Step 4: Calculate the standard deviation
The standard deviation \(\sigma\) is the square root of the variance:
\[
\sigma = \sqrt{10.16} \approx 3.19
\]

### Answer
The standard deviation of the masses of the chicken eggs is approximately **3.19**.

Would you like further details on any specific step or have other questions?

### Related Questions:
1. How is the variance different from the standard deviation in interpretation?
2. What would happen to the standard deviation if all values were increased by 10?
3. How would you calculate the variance if the data set included an additional value?
4. Can standard deviation ever be negative? Why or why not?
5. How does sample size affect the reliability of standard deviation?

### Tip:
Always square deviations when calculating variance to avoid canceling out positive and negative differences.

Find the standard deviation of the masses of chicken eggs shown below, with the mean mass given as 71.2 and five values of x: 67, 74, 68, 75, and 72.

Step-by-step guide to finding the standard deviation of chicken egg masses with a mean of 71.2 grams and sample values of 67, 74, 68, 75, and 72. This tutorial covers key statistical concepts, including variance and standard deviation calculation.

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