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 the empirical relationship: \[\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\] Given Mode = 10: \[10 = 3 \times \text{Median} - 2 \times \text{Mean}\] Also, \[\text{Mean} + \text{Median} = 25\] Let Mean = \(x\) and Median = \(y\): \[10 = 3y - 2x\] and \[x + y = 25\] Solving: From the second equation: \[x = 25 - y\] Substituting into the first equation: \[10 = 3y - 2(25 - y)\] \[10 = 3y - 50 + 2y\] \[5y = 60\] \[y = 12\] \[x = 25 - 12 = 13\] Therefore, Mean = 13, Median = 12