1. Average monthly salary of all staff together

Given:

• Average salary of 10 male staff = Rs. 20,000
• Average salary of 5 female staff = Rs. 18,000

Solution:
The formula for the combined average salary is:

$$\text{Combined Average} = \frac{\text{Total Salary of Male Staff + Total Salary of Female Staff}}{\text{Total Number of Staff}}$$ $$\text{Total salary of male staff} = 10 \times 20,000 = 200,000$$
$$\text{Total salary of female staff} = 5 \times 18,000 = 90,000$$
$$\text{Combined Average} = \frac{200,000 + 90,000}{10 + 5} = \frac{290,000}{15} = 19,333.33$$

Answer: The average monthly salary of all staff together is Rs. 19,333.33.

2. Standard deviation and variance of the data

Given:

• Mean = 12
• Coefficient of Variation (CV) = 25%

Formula:

$$CV = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100$$
$$\text{Standard Deviation} = \frac{CV \times \text{Mean}}{100}$$ $$\text{Standard Deviation} = \frac{25 \times 12}{100} = 3$$

Variance is the square of the standard deviation:

$$\text{Variance} = (\text{Standard Deviation})^2 = 3^2 = 9$$

Answer:

• Standard deviation = 3
• Variance = 9

3. Classification of data in statistics

Definition:
Classification of data refers to the process of arranging data into different categories or classes based on shared characteristics. It helps in simplifying, organizing, and analyzing data effectively.

4. Finding Mean

• Mean = 40
• Mode = 30

$$\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$$

Rearranging to solve for Median:

$$\text{Median} = \frac{\text{Mode} + 2 \times \text{Mean}}{3}$$

Substitute the values:

$$\text{Median} = \frac{30 + 2 \times 40}{3} = \frac{30 + 80}{3} = \frac{110}{3} = 36.67$$