JEE Mains · Maths · STD 11 - 13. statistics
The mean age of \(25\) teachers in a school is \(40\, years\). A teacher retires at the age of \(60\, years\) and a new teacher is appointed in his place. If now the mean age of the teachers in this school is \(39\, years\), then the age (in years) of the newly appointed teacher is
- A \(25\)
- B \(30\)
- C \(35\)
- D \(40\)
Answer & Solution
Correct Answer
(C) \(35\)
Step-by-step Solution
Detailed explanation
\(\frac{{{x_1} + {x_2} + ... + {x_{25}}}}{{25}} = \bar x = 40\) \( \Rightarrow {x_1} + {x_2} + ... + {x_{25}} = 1000\) Let \(A\) be the age of new teacher. \(\therefore {x_1} + {x_2} + ... + {x_{25}} - 60 + A = 39 \times 25\) \( \Rightarrow 1000 - 60 + A = 975\)…
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