The image contains multiple data tables and problems. Let’s address each question systematically:

1. Arithmetic Mean Calculation

Question: Calculate the Arithmetic Mean of the given data.

Table:

Marks | No. of Students
10 | 10
20 | 25
30 | 30
40 | 30
50 | 5

To calculate the Arithmetic Mean ($\overline{x}$), we use the formula: $\overline{x} = \frac{\sum (f \cdot x)}{\sum f}$ Where:

• $f$ = frequency (No. of Students)
• $x$ = marks

Step 1: Calculate $\sum f$ (Total Frequency)

$\sum f = 10 + 25 + 30 + 30 + 5 = 100$

Step 2: Calculate $\sum (f \cdot x)$

$\sum (f \cdot x) = 100 + 500 + 900 + 1200 + 250 = 2950$

Step 3: Calculate Arithmetic Mean

$\overline{x} = \frac{\sum (f \cdot x)}{\sum f} = \frac{2950}{100} = 29.5$

Answer: The Arithmetic Mean is 29.5.

2. Histogram Representation

Question: Represent the following data using a histogram.

Data:

Daily Wages (in rupees) | No. of Workers
10-15 | 7
15-20 | 19
20-25 | 28
25-30 | 20
30-35 | 12
35-40 | 12
40-45 | 12
45-50 | 20

For a histogram:

• The horizontal axis represents Daily Wages (Class Intervals).
• The vertical axis represents No. of Workers (Frequency).
• Draw rectangles with heights proportional to the frequency and widths equal to the class intervals.

Would you like help sketching this histogram, or should we move to the next problem?

Follow-up Questions:

1. Can you explain how the concept of the Arithmetic Mean applies in real-world contexts?
2. What other types of graphs could be used to represent grouped frequency data?
3. How would the calculation of the Arithmetic Mean change if the data were ungrouped?
4. What is the purpose of a histogram, and how does it differ from a bar chart?
5. Can you suggest scenarios where a histogram might not be the best way to represent data?

Tip:

When calculating the Arithmetic Mean for grouped data, ensure all class intervals have the same width for simplicity unless the question specifies otherwise.