The problem asks to calculate the mean, variance, and standard deviation using the provided frequency distribution. I'll use the formulas for these calculations based on the frequency table.

Given Data:

• Time intervals and their midpoints $x_c$
• Number of employees (frequency) $f$
• The values of $f \times x_c$ (which we'll use for the mean)
• The values of $f \times x_c^2$ (which we'll use for variance)

Steps to calculate:

1. Mean ($\mu$):

$\mu = \frac{\sum f x_c}{\sum f}$ Where:

• $f x_c$ = 18 + 130.5 + 147 + 138 + 89
• $\sum f$ = Total number of employees

2. Variance ($\sigma^2$):

$\sigma^2 = \frac{\sum f x_c^2}{\sum f} - \mu^2$ Where:

• $f x_c^2$ = 81 + 1892.25 + 3601.5 + 4761 + 3960.5

3. Standard Deviation ($\sigma$):

$\sigma = \sqrt{\sigma^2}$

Let me calculate these step by step.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through the manual steps to solve the problem, or try something else?

Here are some related questions:

1. How do we calculate the mean from a frequency table?
2. What role does variance play in understanding data?
3. How does standard deviation differ from variance?
4. Why is it important to find the midpoint in grouped frequency distributions?
5. What are other methods to calculate variance for different data types?

Tip: Always cross-check your intermediate results, especially when dealing with sums in statistics.