Question

A gymnasium weighs all the people that come in to exercise. On one morning, it notes down the weights of 5 people in kgs as follows :

58 kgs, 75 kgs, 83.3 kgs, 83 kgs, 75.7 kgs

The average of their weight is calculated.

If a new person now comes in to exercise, and the new average is calculated to be 76.5, then what was the weight of the new person?​

Answer 1

Answer:

answer for the given problem is given

Answer 2

The weights of 5 people are noted down, and they are 58 Kgs, 75 Kgs, 83.3 Kgs, 83 Kgs and 75.7 Kgs.

To find the average of these five weights, we need to divide the total of the five weights and divide it by 5, since the total number of weights we're finding is 5.

$\rm \Longrightarrow Average \ of \ 5 \ Weights = \dfrac{Sum \ of \ all \ the \ weights}{Total \ number \ of \ weights}$

$\rm \Longrightarrow Average \ of \ 5 \ Weights = \dfrac{58 + 75 + 83.3 + 83 + 75.7}{5}$

$\rm \Longrightarrow Average \ of \ 5 \ Weights = \dfrac{58 + 75 + 83 + 159}{5}$

$\rm \Longrightarrow Average \ of \ 5 \ Weights = \dfrac{375}{5}$

$\rm \Longrightarrow Average \ of \ 5 \ Weights = 75$

Now, one more person joins the exercise, thus the total number of people exercising becomes 6.

Now, the average of the 6 people's weights becomes 76.5, and we are asked to find the weight of the new person.

Let the weight of the new person be w.

$\rm \Longrightarrow Average \ of \ 6 \ Weights = \dfrac{Sum \ of \ all \ the \ weights}{Total \ number \ of \ weights}$

$\rm \Longrightarrow 76.5 = \dfrac{w + 58 + 75 + 83.3 + 83 + 75.7}{6}$

$\rm \Longrightarrow 76.5 = \dfrac{w + 375}{6}$

$\rm \Longrightarrow 76.5 \times 6 = w + 375$

$\rm \Longrightarrow 459 = w + 375$

$\rm \Longrightarrow w = 459 - 375$

$\rm \Longrightarrow w = 84 \ Kg$

Therefore, the weight of the new person is 84 Kgs.