Question

The mean weight of $6$ boys in a group is $48$kg. The individual weights of $5$ of them are $50kg,45kg,49kg,46kg$ and $44kg$. Find the weight of the sixth boy.

Answer 1

Hint: Here we have to find the weight of the sixth boy. First we have to group the mean weight of $6$ boys and then assume the sixth boy. By using the formula to solve them and us get the required answer.

Formula used: Mean weight of the boys $ = \dfrac{{{\text{Total weight of boys}}}}{{{\text{No}}{\text{. of boys}}}}$

Complete step-by-step solution:
It is given that the total number of boys in a group is $48kg$
Let the weight of the $5$ boys from the group are as $50kg,45kg,49kg,46kg$ and $44kg.$
Now we have to find the weight of the sixth boy.
It is given that the mean weight of $6$ boys in the group is $48kg.$
That means weight of the $6$ boys group $ = 48kg$
We know mean weight of boys $ = \dfrac{{{\text{Total weight of all boys}}}}{{{\text{No}}{\text{. of boys}}}}....(1)$
Let the weight of the sixth boy is $a$ kg.
Substitute the values in the above mean formula, we get
$ \Rightarrow \dfrac{{50 + 45 + 49 + 46 + 44 + a}}{6} = 48$
Now adding the numerator values
$ \Rightarrow \dfrac{{234 + a}}{6} = 48$
We just cross multiply the terms
$ \Rightarrow 234 + a = 48 \times 6$
Now we are multiplying the right handed term and
We get,
$ \Rightarrow 234 + a = 288$
Now keeping left handed side and take the numerical value to the right hand side
We can write it as,
$ \Rightarrow a = 288 - 234$
Now by subtraction, we get
$a = 54$

Therefore Weight of the $6^{th}$ boy is $54kg$.

Note: The mean of the series of numbers or observations ${a_1},{a_2},{a_3},{a_4},{a_5}..............{a_n}$ Is given as $\dfrac{{{a_1} + {a_2} + {a_3} + ....... + {a_n}}}{n}$$ = \dfrac{{\sum\limits_{i = 1}^n {{a_i}} }}{n}$, where $n$ is the number of the value in the series.
We need to remember that to have a good understanding of how to compute the average of some numbers.
Also we should be able to solve linear equations in one variable which helps us in simplification of the problem and reach the correct answer.