Chapter 10.1, Problem 14PPS

a.

To determine

To calculate which contestant falls on sixth decile.

Answer to Problem 14PPS

D and F are at 6^th decile.

Explanation of Solution

Given information: Scores of the contestants.

Formula Used: Decile is,

  $D_i=(n+1)\frac{i}{10}$

Calculation:

Arranging the values in a descending order

Name	Score
D	29
V	28
I	27
N	26
B	25
W	22
C	21
J	20
Y	18
A	17
K	16
F	15
D	14
H	12
I	11
M	10
B	9
T	6
H	5
P	4

Substituting the values in decile formula,

  $D_6=(20+1)\frac{6}{10}$

So,

  $D_6=(21)\frac{6}{10}$

On solving,

  $D_6=12.6$

Hence, comparing the value to the table. So, D and F are at 6^th decile.

Conclusion: D and F are at 6^th decile.

b.

To determine

To calculate the decile of H and D

Answer to Problem 14PPS

D is at 6^th decile and H is at 7^th decile

Explanation of Solution

Given information: Scores of contestants

Name	Score
D	29
V	28
I	27
N	26
B	25
W	22
C	21
J	20
Y	18
A	17
K	16
F	15
D	14
H	12
I	11
M	10
B	9
T	6
H	5
P	4

Formula Used:

Decile is,

  $D_i=(n+1)\frac{i}{10}$

Calculation:

For H,

Substituting the values,

  $14=(20+1)\frac{i}{10}$

So,

  $14=(21)\frac{i}{10}$

Cross- multiplying,

  $i=14\times \frac{10}{21}$

On solving,

  $i=6.67$

Rounding of the value,

  $\approx 7$

Hence, H is at 7^th decile

And from part (i) we know D is at 6^th decile

Conclusion: D is at 6^th decile and H is at 7^th decile