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To find the median for the given frequency distribution, we will follow these steps:

### Step 1: Identify the Total Number of Employees
Sum of the number of employees:
\[
\text{Total number of employees} = 10 + 70 + 80 + 100 + 150 + 90 = 500
\]
So, \( N = 500 \).

### Step 2: Calculate the Cumulative Frequency (C.F.)
The cumulative frequency is the running total of the frequencies:
- For the first class (0-50): \( 10 \)
- For the second class (50-100): \( 10 + 70 = 80 \)
- For the third class (100-150): \( 80 + 80 = 160 \)
- For the fourth class (150-200): \( 160 + 100 = 260 \)
- For the fifth class (200-250): \( 260 + 150 = 410 \)
- For the sixth class (250-300): \( 410 + 90 = 500 \)

### Step 3: Find the Median Class
The median is located at the \( \frac{N}{2} \)th value, which is:
\[
\frac{500}{2} = 250
\]
The cumulative frequency just greater than 250 is 260, which corresponds to the class \( 150-200 \). Therefore, the median class is \( 150-200 \).

### Step 4: Apply the Median Formula
The formula for the median is:
\[
\text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times h
\]
Where:
- \( L \) is the lower boundary of the median class = 150
- \( F \) is the cumulative frequency before the median class = 160
- \( f \) is the frequency of the median class = 100
- \( h \) is the class width = 50 (since the width of each class interval is 50)

Substituting the values into the formula:
\[
\text{Median} = 150 + \left( \frac{250 - 160}{100} \right) \times 50
\]
\[
\text{Median} = 150 + \left( \frac{90}{100} \right) \times 50
\]
\[
\text{Median} = 150 + 0.9 \times 50
\]
\[
\text{Median} = 150 + 45 = 195
\]

### The Median is 195 Rs.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does the cumulative frequency help in identifying the median class?
2. What would happen to the median if we added another class interval?
3. How is the formula for the median derived in frequency distributions?
4. Can the median be found directly without using the formula? Why or why not?
5. How does changing the class width affect the median?

**Tip:** Always make sure the class intervals are continuous (no gaps) when calculating the median in frequency distributions.

Find the median for the given frequency distribution: 
Wages in Rs.: 0-50, 50-100, 100-150, 150-200, 200-250, 250-300 
Number of employees: 10, 70, 80, 100, 150, 90

Learn how to find the median for a given frequency distribution of wages of employees. This problem uses the median formula, cumulative frequency, and class intervals to find the median wage from the dataset provided. Suitable for high school students in Grades 9-12.

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