The final score of a figure skating competition is determined by finding the average of six judges' scores. Write a formula for the average A
of six scores x1, x2, x3, x4, x5, and x6. Then solve the formula for x4, the fourth judge's score.
A=

x4=

The table shows the scores given to a figure skater by the judges. The skater receives a final score of 5.7. Find the score given by the fourth judge.

Judge 1 2 3 4 5 6
Score 5.6 5.8 5.6 x4 5.9 5.4

[tex]\text{\bold{Average of Scores}} = \frac{\text{Sum of all scores}}{\text{Total Number of scores}}\\\\ = \frac{x_1+x_2+ x_3+ x_4+ x_5+ x_6}{6}[/tex]

If we want to compute the score of fourth judge, we can rearrange the above equation to get [tex]x_4[/tex]

[tex]x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)[/tex]

b) Average score given = 5.7

Judge: 1 2 3 4 5 6

Score: 5.6 5.8 5.6 x 5.9 5.4

Putting the value in the the above equation, we get,

[tex]x = 6(5.7) - (5.6+5.8+5.6+5.9+5.4)[/tex]

x = 5.9

Thus, the score given by fourth judge is 5.9

[tex]x_4 = 5.9[/tex]

joaobezerra joaobezerra · Answer 2 · 2021-09-17T16:59:37+02:00

Using the mean concept, it is found that:

The average is given by [tex]A = \frac{x1 + x2 + x3 + x4 + x5 + x6}{6}[/tex]

The fourth judge's score is x4 = 5.9.

---------------------------

The mean, which is the average A, is given by the sum of all scores divided by the number of scores.
There are 6 scores, x1, x2, x3, x4, x5 and x6.
Thus, the average is:

[tex]A = \frac{x1 + x2 + x3 + x4 + x5 + x6}{6}[/tex]

---------------------------

Average of 5.7, thus, [tex]A = 5.7[/tex]
The grades are: [tex]x1 = 5.6, x2 = 5.8, x3 = 5.6, x5 = 5.9, x6 = 5.4[/tex]

To find x4, we replace into the equation for the average, thus:

[tex]A = \frac{x1 + x2 + x3 + x4 + x5 + x6}{6}[/tex]

[tex]5.7 = \frac{5.6 + 5.8 + 5.6 + x4 + 5.9 + 5.4}{6}[/tex]

[tex]28.3 + x4 = 34.2[/tex]

[tex]x4 = 34.2 - 28.3[/tex]

[tex]x4 = 5.9[/tex]

The fourth judge's score is x4 = 5.9.

A similar problem is given at https://brainly.com/question/21133998