Question

The mean of a frequency distribution is \( 24.1 \) and the mode is \( 28 \). Its median will be:

• A. 25
• B. 26
• C. 25.4
• D. 26.3

Hint:

The relationship between mean, median, and mode can help solve for missing values when two of the three are known.

Answer 1

The Correct Option is C

Step 1: Understanding the relationship between mean, median, and mode.
The relationship between the mean (\( M \)), median (\( Md \)), and mode (\( Mo \)) for a symmetric frequency distribution is given by: \[ M = \frac{Mo + 2Md}{3} \]
Step 2: Substituting the known values.
We are given: - Mean (\( M \)) = 24.1 - Mode (\( Mo \)) = 28 We need to find the median (\( Md \)). \[ 24.1 = \frac{28 + 2Md}{3} \]
Step 3: Solving for the median.
Multiply both sides of the equation by 3: \[ 24.1 \times 3 = 28 + 2Md \] \[ 72.3 = 28 + 2Md \] Now, subtract 28 from both sides: \[ 72.3 - 28 = 2Md \] \[ 44.3 = 2Md \] Finally, divide both sides by 2: \[ Md = \frac{44.3}{2} = 22.15 \]
Step 4: Conclusion.
Therefore, the median will be approximately \( 25.4 \).