Question

The mean of the following table will be 

• A. 21
• B. 23
• C. 25
• D. 26

Hint:

Always find midpoints for grouped data before applying the formula \(\bar{x} = \frac{\Sigma fx}{\Sigma f}\).

Answer 1

The Correct Option is C

Step 1: Find midpoints of each class.
\[ \text{Midpoints (x)}: 5, 15, 25, 35 \]
Step 2: Multiply frequency and midpoint.
\[ fx = (2 \times 5) + (1 \times 15) + (4 \times 25) + (3 \times 35) = 10 + 15 + 100 + 105 = 230 \]
Step 3: Find total frequency.
\[ \Sigma f = 2 + 1 + 4 + 3 = 10 \]
Step 4: Calculate mean.
\[ \text{Mean} = \frac{\Sigma fx}{\Sigma f} = \frac{230}{10} = 23 \]
Step 5: Conclusion.
Hence, the mean of the data is 23.