Q - 5-15:8
Ans - 12.5
Q - 15-25:12
Ans - 5:6
Q - 25-35:15
Ans - 2:3
Q - 35-45:9
Ans - 10:9
Q - 45-55:6
Ans - 10:6

Understanding the Data
The given data represents frequency distribution in class intervals with respective frequencies:
- 5-15: 8
- 15-25: 12
- 25-35: 15
- 35-45: 9
- 45-55: 6
Step 1: Find Midpoints
To calculate the arithmetic mean using the shortcut method, we first need to find the midpoints (x) of each class interval:
- Midpoint for 5-15: (5 + 15) / 2 = 10
- Midpoint for 15-25: (15 + 25) / 2 = 20
- Midpoint for 25-35: (25 + 35) / 2 = 30
- Midpoint for 35-45: (35 + 45) / 2 = 40
- Midpoint for 45-55: (45 + 55) / 2 = 50
Step 2: Create a Table
Here’s how the data looks in tabular form:
- Class Interval: 5-15, 15-25, 25-35, 35-45, 45-55
- Frequency (f): 8, 12, 15, 9, 6
- Midpoint (x): 10, 20, 30, 40, 50
- f * x: 80, 240, 450, 360, 300
Step 3: Calculate Σf and Σ(f * x)
- Σf = 8 + 12 + 15 + 9 + 6 = 50
- Σ(f * x) = 80 + 240 + 450 + 360 + 300 = 1430
Step 4: Calculate the Arithmetic Mean
Using the formula for the arithmetic mean:
\[
\text{Mean} = \frac{\Sigma(f \cdot x)}{\Sigma f} = \frac{1430}{50} = 28.6
\]
Conclusion
The arithmetic mean of the given data is 28.6. This method effectively simplifies the calculation of the mean from grouped data.