Question

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

Answer 1

The average A is written as the sum of the scores awarded by each judge, among the number of judges.

Therefore $A =\frac{x1 + x2 + x3 + x4 + x5 + x6}{6}$

We can know the score awarded by judge number 4 if we know the final average score (A) and the score awarded by the other 5 judges.

The final score A is 5.7

The score awarded by judge 1, 2, 3, 5, and 6 is 5.6; 5.8; 5.6; 5.9; 5.4 respectively.

Then we have all the necessary information to find x4:

$x4=6A-x1-x2-x3-x5-x6$

$x4=6*5.7 -5.6-5.8-5.6-5.9-5.4$

$x4=5.9$

Then the score of the fourth judge was $x4=5.9$

Answer 2

Answer:

a)  $\text{Average of Scores} = \frac{\text{Sum of all scores}}{\text{Total Number of scores}}\\\\ = \frac{x_1+x_2+ x_3+ x_4+ x_5+ x_6}{6}$

$x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)$

b)$x_4 = 5.9$

Step-by-step explanation:

a)The judges have given six scores as: $x_1, x_2, x_3, x_4, x_5, x_6$

We have to find the average of these scores:

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

If we want to compute the score of fourth judge, we can rearrange the above equation to get $x_4$

$x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)$

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,

$x = 6(5.7) - (5.6+5.8+5.6+5.9+5.4)$

x = 5.9

Thus, the score given by fourth judge is 5.9

$x_4 = 5.9$