Question

The mean weight per student in a group of 7 students is 55kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student (in Kg).

Answer 1

Hint: First we will find the total weight of 7 students by using the mean formula. After that, we will calculate the total weight of 6 students. Then subtract the total weight of 6 students from the total weight of 7 students to calculate the weight of the seventh student.

Formula Used:
${\rm{Mean = }}\dfrac{{{\rm{Sum}}\,{\rm{of}}\,{\rm{terms}}}}{{{\rm{Number}}\,{\rm{of}}\,{\rm{terms}}}}$

Complete step by step solution:
In a class of seven students, the average weight is 55 kg. Six of them have individual weights in kilograms of 52, 54, 55, 53, 56, and 54.
Now apply the mean formula.
${\rm{Mean = }}\dfrac{{{\rm{The}}\,{\rm{sum}}\,\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{students}}}}{{{\rm{Number}}\,{\rm{of}}\,{\rm{students}}}}$
Put the value of mean and number of students
$ \Rightarrow {\rm{55 = }}\dfrac{{{\rm{The}}\,{\rm{sum}}\,\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{students}}}}{{\rm{7}}}$
Multiply 7 with both sides
$ \Rightarrow {\rm{55}} \times {\rm{7 = The}}\,{\rm{sum}}\,\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{students}}$
$ \Rightarrow {\rm{The}}\,{\rm{sum}}\,\,{\rm{of}}\,{\rm{weight}}\,{\rm{of}}\,{\rm{students}} = 385$
The sum of the weight of 6 students is $52 + 54 + 55 + 53 + 56 + 54 = 324$
Subtract the weight of 6 students from the weight of 7 students:
The weight of ${7^{th}}$ is $385 - 324 = 61$

The weight of the seventh student 61 kg.

Note: Remember that mean weight of student is $= \dfrac{\text{Sum of weights of students}}{\text{ Number of students}}$. Here the weight of the student may be less than or greater than the mean.