https://file.aiquickdraw.com/mathbot/file/17288154852695v6f6zya.jpg

To compute the **arithmetic mean** of the salaries from the given distribution, we need to follow these steps:

### Step 1: Identify the midpoints (class marks) of each salary class
The midpoint for each class interval is calculated by taking the average of the lower and upper boundaries of each class.

\[
\text{Midpoint} = \frac{\text{Lower limit} + \text{Upper limit}}{2}
\]

Here are the class intervals and their midpoints:

- \(0 - 500\): Midpoint = \(\frac{0 + 500}{2} = 250\)
- \(500 - 1000\): Midpoint = \(\frac{500 + 1000}{2} = 750\)
- \(1000 - 1500\): Midpoint = \(\frac{1000 + 1500}{2} = 1250\)
- \(1500 - 2000\): Midpoint = \(\frac{1500 + 2000}{2} = 1750\)
- \(2000 - 2500\): Midpoint = \(\frac{2000 + 2500}{2} = 2250\)
- \(2500 - 3000\): Midpoint = \(\frac{2500 + 3000}{2} = 2750\)
- \(3000 - 3500\): Midpoint = \(\frac{3000 + 3500}{2} = 3250\)
- \(3500 - 4000\): Midpoint = \(\frac{3500 + 4000}{2} = 3750\)
- \(4000 - 4500\): Midpoint = \(\frac{4000 + 4500}{2} = 4250\)

### Step 2: Multiply the midpoints by the number of employees
Now we multiply each midpoint by the corresponding number of employees in that salary range:

\[
\text{Mean contribution} = \text{Midpoint} \times \text{No. of employees}
\]

\[
\begin{array}{|c|c|c|}
\hline
\text{Salary Class} & \text{Midpoint (x)} & \text{No. of Employees (f)} & f \times x \\
\hline
0 - 500     & 250  & 6  & 250 \times 6 = 1500  \\
500 - 1000  & 750  & 8  & 750 \times 8 = 6000  \\
1000 - 1500 & 1250 & 12 & 1250 \times 12 = 15000 \\
1500 - 2000 & 1750 & 25 & 1750 \times 25 = 43750 \\
2000 - 2500 & 2250 & 25 & 2250 \times 25 = 56250 \\
2500 - 3000 & 2750 & 20 & 2750 \times 20 = 55000 \\
3000 - 3500 & 3250 & 12 & 3250 \times 12 = 39000 \\
3500 - 4000 & 3750 & 8  & 3750 \times 8 = 30000 \\
4000 - 4500 & 4250 & 2  & 4250 \times 2 = 8500  \\
\hline
\end{array}
\]

### Step 3: Sum up the products and the number of employees
- Total sum of \(f \times x\) = \(1500 + 6000 + 15000 + 43750 + 56250 + 55000 + 39000 + 30000 + 8500 = 253000\)
- Total number of employees = \(6 + 8 + 12 + 25 + 25 + 20 + 12 + 8 + 2 = 118\)

### Step 4: Calculate the arithmetic mean
The arithmetic mean is given by:

\[
\text{Mean} = \frac{\sum(f \times x)}{\sum f}
\]

Substituting the values:

\[
\text{Mean} = \frac{253000}{118} = 2144.07
\]

### Conclusion:
The **arithmetic mean** of the salaries is approximately **₹2144.07**.

Would you like any more details or have any questions?

---

Here are 5 related questions to expand on this topic:
1. How would the mean change if one of the salary ranges had more employees?
2. What is the significance of the midpoint in calculating the mean?
3. How can we use this information to find the median salary?
4. What would happen to the mean if there were a higher range of salaries?
5. How does the arithmetic mean differ from the median in salary distributions?

**Tip:** When working with grouped data like this, always remember to verify the midpoints and class intervals before performing calculations to avoid errors.

Compute the arithmetic mean of the monthly salaries of employees from the given distribution.

Learn how to compute the arithmetic mean of monthly salaries from a grouped data distribution. This problem involves statistical concepts such as class midpoints and the mean formula, making it ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation