Question

If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are

• A. 12 and 13
• B. 13 and 12
• C. 10 and 15
• D. 15 and 10

Hint:

Use the empirical relation: Mode = 3 Median - 2 Mean in grouped data.

Answer 1

The Correct Option is A

Using empirical relation: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] Substituting Mode = 10: \[ 10 = 3 \times \text{Median} - 2 \times \text{Mean} \] Also, given: \[ \text{Mean} + \text{Median} = 25 \] Let Mean = \(x\) and Median = \(y\) \[ 10 = 3y - 2x \] and \[ x + y = 25 \] Solving: From 2nd equation: \[ x = 25 - y \] Substituting in 1st: \[ 10 = 3y - 2(25 - y) \] \[ 10 = 3y - 50 + 2y \] \[ 5y = 60 \] \[ y = 12 \] \[ x = 25 - 12 = 13 \] So, Mean = 13, Median = 12