If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectivel…

Question

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

Accepted Answer

## Model Answer Using the empirical relation: **Mode = 3 Median – 2 Mean** Given: Mode = 10, Mean + Median = 25 Let Mean = $x$, Median = $25 - x$ $10 = 3(25 - x) - 2x$ $10 = 75 - 3x - 2x$ $5x = 65$ $x = 13$ ∴ Mean = **13** and Median = **12** → **Option B** ## Explanation The key formula from the textbook (Chapter 13, Remarks after Section 13.4) is the empirical relationship: **3 Median = Mode + 2 Mean**. Set up two equations using this and Mean + Median = 25, then solve simultaneously. Examiners expect you to recall and apply this formula directly.

Mathematics — Standard (041) — CBSE Class 10 board question