Question

The mean of the following table will be:

• A. 21
• B. 20.6
• C. 20
• D. 19.6

Hint:

To find the mean from a frequency distribution, multiply each class midpoint by its frequency, sum these products, and divide by the total frequency.

Answer 1

The Correct Option is B

Step 1: Find the class midpoints.
The class midpoints \( x \) for each class interval are: \[ \text{Midpoint of } 0-10 = \frac{0 + 10}{2} = 5 \] \[ \text{Midpoint of } 10-20 = \frac{10 + 20}{2} = 15 \] \[ \text{Midpoint of } 20-30 = \frac{20 + 30}{2} = 25 \] \[ \text{Midpoint of } 30-40 = \frac{30 + 40}{2} = 35 \] \[ \text{Midpoint of } 40-50 = \frac{40 + 50}{2} = 45 \]
Step 2: Multiply each midpoint by its corresponding frequency.
Now multiply the midpoints by their respective frequencies: \[ 5 \times 6 = 30, \quad 15 \times 6 = 90, \quad 25 \times 6 = 150, \quad 35 \times 3 = 105, \quad 45 \times 1 = 45 \]
Step 3: Find the sum of the products.
The sum of the products is: \[ 30 + 90 + 150 + 105 + 45 = 420 \]
Step 4: Find the total frequency.
The total frequency is: \[ 6 + 6 + 6 + 3 + 1 = 22 \]
Step 5: Calculate the mean.
The mean is given by: \[ \text{Mean} = \frac{\text{Sum of products}}{\text{Total frequency}} = \frac{420}{22} \approx 20.6 \]
Step 6: Conclusion.
Thus, the mean of the given data is 20.6. Therefore, the correct answer is (B).