Question

The mode and mean of a data are 7 and 5 respectively, then median is:

• A. 12
• B. \( \frac{17}{3} \)
• C. 4
• D. \( \frac{2}{3} \)

Hint:

The empirical relation \( \mu = \frac{\text{mode} + 2 \times \text{median}}{3} \) helps to find the median when the mean and mode are known.

Answer 1

The Correct Option is B

Step 1: Use the empirical relationship between mean, median, and mode
- The empirical relationship between the mean (\( \mu \)), mode (\( \text{mode} \)), and median (\( \text{median} \)) is given by: \[ \mu = \frac{\text{mode} + 2 \times \text{median}}{3} \] Step 2: Substitute the given values
We are given that:
Mode = 7,
Mean = 5.
Substitute these values into the equation: \[ 5 = \frac{7 + 2 \times \text{median}}{3} \] Step 3: Solve for median
Multiply both sides by 3 to eliminate the denominator: \[ 15 = 7 + 2 \times \text{median} \] Subtract 7 from both sides: \[ 8 = 2 \times \text{median} \] Now, divide by 2: \[ \text{median} = \frac{8}{2} = 4 \] Thus, the median is \( 4 \).