\text{Sum} = 42,090 + 51,930 + 53,910 + 56,630 + 61,050 + 61,220 = 326,830

Question

\]

The number of data points (n) is 6.

Now, calculate the mean:

\[
\text{Mean} = \frac{\text{Sum}}{n} = \frac{326,830}{6} \approx 54,471.67
\]

### Step 2: Find the squared differences from the mean

Now, let's calculate the squared differences for each salary:

1. \( (42,090 - 54,471.67)^2 \approx (−12,381.67)^2 \approx 153,238,062.79 \)
2. \( (51,930 - 54,471.67)^2 \approx (−2,541.67)^2 \approx 6,451,111.11 \)
3. \( (53,910 - 54,471.67)^2 \approx (−561.67)^2 \approx 315,111.11 \)
4. \( (56,630 - 54,471.67)^2 \approx (2,158.33)^2 \approx 4,661,111.11 \)
5. \( (61,050 - 54,471.67)^2 \approx (6,578.33)^2 \approx 43,352,111.11 \)
6. \( (61,220 - 54,471.67)^2 \approx (6,748.33)^2 \approx 45,486,111.11 \)

### Step 3: Calculate the average of the squared differences

Now we sum these squared differences:

\[
\text{Total squared differences} = 153,238,062.79 + 6,451,111.11 + 315,111.11 + 4,661,111.11 + 43,352,111.11 + 45,486,111.11 \approx 253,473,517.33
\]

Finally, to find the variance, divide by the number of values \( n \):

\[
\text{Variance} = \frac{\text{Total squared differences}}{n} = \frac{253,473,517.33}{6} \approx 42,245,586.22
\]

### Result

The variance of the occupation salaries is approximately **42,245,586.22**. What is the standard deviation?

Answer 1

To find the standard deviation, you take the square root of the variance.

Given that the variance is approximately 42,245,586.22, we can calculate the standard deviation as follows:

\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{42,245,586.22} \approx 6,499.76 \]

Result

The standard deviation of the occupation salaries is approximately 6,499.76.