Chapter 10.1, Problem 14IP

To determine

To calculate: the lowest score for required average.

Answer to Problem 14IP

Least required score from 14^th judge to win the competition is $4.5$ .

Explanation of Solution

Given information:

1. Mean score from 13 judges was 5.9.
2. Need to determine lowest score from 14^th judge for average of 5.8.

Formula used:

1) $\text{mean=}\frac{\text{Sum}\text{of}\text{the}\text{data}}{\text{number}\text{of}\text{items}\text{in}\text{data}\text{set}}$

.

Calculation:

Mean from 13 judges $=5.9$

using $\text{mean=}\frac{\text{Sum}\text{of}\text{the}\text{data}}{\text{number}\text{of}\text{items}\text{in}\text{data}\text{set}}$

Mean of 13 judges score $=\frac{\text{Sum}\text{of}\text{the}\text{score}\text{of}\text{13}\text{judges}}{\text{13}}$

  $5.9=\frac{\text{Sum}\text{of}\text{the}\text{score}\text{of}\text{13}\text{scores}}{\text{13}}$

  $5.9\times 13=\text{Sum}\text{of}\text{the}\text{score}\text{of}\text{13}\text{judges}$

  $\text{Sum}\text{of}\text{the}\text{score}\text{of}\text{13}\text{judges}=76.7$

Assume score given by 14^th judge be represented by variable $x$ .

Required Average of 14 judges = Mean from 14 judges $=5.8$

Mean of 14 judges score $=\frac{\text{Sum}\text{of}\text{the}\text{score}\text{of}\text{14}\text{scores}}{\text{14}}$

  $5.8=\frac{\text{Sum}\text{of}\text{the}\text{score}\text{of}\text{13}\text{scores+}x}{\text{14}}$

  $5.8=\frac{\text{76}\text{.7 +}x}{\text{14}}$

  $5.8\times 14=\text{76}\text{.7 +}x$

  $81.2-\text{76}\text{.7}=x$

  $x=4.5$

Hence least required score from 14^th judge to win the competition is $4.5$ .