Question

mean of weight of 50 students In a class is 40 Kg if the weight of teacher is added mean is increased by 500 find the weight of the teacher​

Answer 1

$\underline{\textbf{\huge{Question}}}$

mean of weight of 50 students In a class is 40 Kg if the weight of teacher is added mean is increased by 500 g find the weight of the teacher​?

$\underline{\textbf{\huge{Answer}}}$

Mean Of 50 Students Weight=50

Let Actual Student Weight=x-1,x2,x3,x4,.......x50

We know

$\boxed{\mathtt{Average=\frac{Sum\:of\:all\:terms}{Total\:Terms}}}$

MEANS

$\boxed{\mathtt{\frac{x_1+x_2+x_3.... +x_{50}}{50}=40}}$

$\boxed{\mathtt{x_1+x_2+x_3.... +x_{50}=40\times50}}$

$\boxed{\mathtt{x_1+x_2+x_3.... +x_{50}=2000}}$

MEANS Actual Weight Of All Students=2000kg

Now Teacher Is Added

Let Teacher Weight=x51

Total Persons Now=51

Mean Increase by 500 g

Now Mean=40.5 kg

$\boxed{\mathtt{\frac{x_1+x_2+x_3.... +x_{51}}{51}=40.5}}$

We know x1...x50=2000

$\boxed{\mathtt{\frac{2000+ x_{51}}{51}=40.5}}$

$\boxed{\mathtt{2000+x_{51}=40.5\times\:51}}$

$\boxed{\mathtt{2000+x_{51}=2065.5\:kg}}$

$\boxed{\mathtt{+x_{51}=2065.5-2000\:kg}}$
=65.5

$\boxed{\mathtt{\huge{Teacher=65.5 kg}}}$

Answer 2

Error correction : "The mean increased by 500 grams."

Since, Mean = (1/n) ∑

Where, ∑ = x₁ + x₂ +......+ xₙ

Here, Mean = 40 kg and n = 50 students

So, 40 =  ∑ / 50

⇒ 2000 = ∑

When teacher weight is added then mean is increased by 500 g or 0.5 kg.

Let's teacher weight be xₐ.

New Mean = Initial Mean + 0.5 kg = 40 + 0.5

New n = 50 + 1 = 51

New sigma = Initial sigma + xₐ

40 + 0.5 = ( ∑ + xₐ ) / 51

40.5 = ( 2000 + xₐ ) / 51

40.5 × 51 = 2000 + xₐ

2,065.5 − 2,000 = xₐ

65.5 kg = xₐ

⇒Answer : 65.5 kg