Question

The mean weight of a class of 35. Students is 45 kg.if the weight of the teacher is addded and the mean weight increases by 500g .find the weight of the teacher

Answer 1

total wt= mean wt* no of students
total wt= 35*45=1575
when teacher also included
(1575+x) =( 45.5)*36=1638
x= 63 kg

Answer 2

The weight of teacher is 63 kg

Step-by-step explanation:

The formula for mean is as follows:

$\text{Mean} =\frac{\text {Sum of all the entities}}{\text {Number of entities}}$

Given that Mean weight of the class = 45

$\Rightarrow \frac{\text {Sum of all the weights of students}}{\text {total number of students}}=45$

Let sum of all the weights of the students be $w_s$

$\frac{w_{s}}{35}=45$

$w_{s}=35 \times 45$

$\Rightarrow w_{s}=1575$

After adding teacher’s weight, the mean weight increases by 500 g

Therefore, mean weight along with teacher = 45 kg + 500 g

As 1 kg = 1000 g; 500 g = ½ kg = 0.5 kg

Mean weight along with teacher = 45 kg + 0.5 kg = 45.5 kg

Therefore, mean weight of the class students along with teacher = 45.5

Also the total number of students including teacher is 35 + 1 = 36

$\frac{\text { Sum of all the weights of students along with teacher}}{\text {total number of students}}=45.5$

Let sum of all weights of students along with teacher be $w_{ts}$

$\frac{w_{t s}}{36}=45.5$

$w_{t s}=36 \times 45.5$

$w_{t s}=1638$

Therefore, weight of the teacher will be the difference of weights of all students including teacher and weight of all students

$\Rightarrow 1638-1575=63 \ kg$