Chapter 10.1, Problem 13PPS

a.

To determine

Final score for each gymnast. Find winner.

Answer to Problem 13PPS

J is winner

Explanation of Solution

Given Information:

	Judge 1	Judge2	Judge 3	Judge 4	Judge5	Judge 6
J	9.6	9.6	9.8	9.4	9.6	9.8
R	9.5	9.3	9.8	9.4	9.2	9.7
L	9.6	9.8	9.4	9.2	9.7	9.4
B	9.4	9.2	9.6	9.8	9.5	9.6
H	9.7	9.3	9.7	9.4	9.3	9.7

Formula used:

Mean= $\frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}$

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms

Calculation:

J after removing highest and lowest value:

Mean= $\frac{9.6+9.6+9.6+9.8}{4}$ = $\frac{38.6}{4}=9.65$

R after removing highest and lowest value:

Mean= $\frac{9.5+9.3+9.4+9.7}{4}=\frac{37.9}{4}=9.47$

L after removing highest and lowest value:

Mean= $\frac{9.6+9.4+9.7+9.4}{4}=\frac{38.1}{4}=9.5$

B after removing highest and lowest value:

Mean= $\frac{9.6+9.4+9.5+9.6}{4}=\frac{38.1}{4}=9.5$

H after removing highest and lowest value:

Mean= $\frac{9.7+9.7+9.3+9.4}{6}=\frac{38.1}{6}=9.5$

J has highest average. He is winner.

b.

To determine

Find winner

Answer to Problem 13PPS

J is winner

Explanation of Solution

Given information:

	Judge 1	Judge2	Judge 3	Judge 4	Judge5	Judge 6
J	9.6	9.6	9.8	9.4	9.6	9.8
R	9.5	9.3	9.8	9.4	9.2	9.7
L	9.6	9.8	9.4	9.2	9.7	9.4
B	9.4	9.2	9.6	9.8	9.5	9.6
H	9.7	9.3	9.7	9.4	9.3	9.7

Formula used:

Mean= $\frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}$

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms

Calculation:

J after removing highest and lowest value:

Mean= $\frac{9.6+9.6+9.6+9.8+9.4+9.8}{6}=\frac{57.8}{6}=9.6$

R after removing highest and lowest value:

Mean= $\frac{9.5+9.3+9.4+9.7+9.2+9.8}{6}=\frac{56.9}{6}=9.43$

L after removing highest and lowest value:

Mean= $\frac{9.6+9.4+9.7+9.4+9.2+9.8}{6}=\frac{57.1}{6}=9.51$

B after removing highest and lowest value:

Mean= $\frac{9.6+9.4+9.5+9.6+9.8+9.2}{6}=\frac{57.1}{6}=9.51$

H after removing highest and lowest value:

Mean= $\frac{9.7+9.7+9.3+9.4+9.7+9.3}{6}=\frac{57.1}{6}=9.51$

J has highest average. He is winner.

c.

To determine

Compare results

Answer to Problem 13PPS

Results are same in both cases

Explanation of Solution

Given Information:

Solutions of above parts

The results if compared with each other on above is same as J wins in both the cases. Even after excluding or including least and highest score, scores are almost same.