the average marks of a class of 35 students is 45 kg . if the mass of teacher be included then the average mass increases by 500g. find the mass of teacher
Answers
Answer:
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}}Mean=
Number of entities
Sum of all the 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⇒
total number of students
Sum of all the weights of students
=45
Let sum of all the weights of the students be w_sw
s
\frac{w_{s}}{35}=45
35
w
s
=45
w_{s}=35 \times 45w
s
=35×45
\Rightarrow w_{s}=1575⇒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
total number of students
Sum of all the weights of students along with teacher
=45.5
Let sum of all weights of students along with teacher be w_{ts}w
ts
\frac{w_{t s}}{36}=45.5
36
w
ts
=45.5
w_{t s}=36 \times 45.5w
ts
=36×45.5
w_{t s}=1638w
ts
=1638
Therefore, weight of the teacher will be the difference of weights of all students including teacher and weight of all students