If the mean of 5 observations (x + 1), (x + 3), (x + 5), (x + 7) and (x + 9) is given as 20, then find the value of the median.
यदि 5 प्रेक्षणों (x + 1), (x + 3), (x + 5), (x + 7) और (x + 9) का माध्य (Mean) 20 दिया गया है, तो माध्यिका (Median) का मान ज्ञात कीजिए।
Answer और ExplanationAnswer and explanation
Answer: (C) 20
योग = 5x + (1 + 3 + 5 + 7 + 9) = 5x + 25
माध्य (Mean) = 5x + 255 = x + 5 = 20 ⇒ x = 15
प्रेक्षण (Observations): 16, 18, 20, 22, 24 (पहले से क्रम में)
माध्यिका (Median) = तीसरा मान (Value) = 20
✓
माध्यिका = 20।
Sum = 5x + (1 + 3 + 5 + 7 + 9) = 5x + 25
Mean = 5x + 255 = x + 5 = 20 ⇒ x = 15
Observations: 16, 18, 20, 22, 24 (already in order)
Median = 3rd value = 20
✓
Median = 20.
SMART APPROACH
प्रेक्षण (Observations) AP में हैं, तो माध्यिका (Median) = माध्य (Mean)। x निकालने की ज़रूरत ही नहीं: माध्यिका = 20।
The observations are in AP, so median = mean. No need to find x: median = 20.
Source: Selection Post Phase XIV (Graduate) · 28 Jul 2025 · Shift 3। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (Graduate) · 28 Jul 2025 · Shift 3. Solution by Prashant Sir, from Vijayastra.