Chapter 10, Problem 12SGR

a.

To determine

To calculate the bowlers are above 50^th

Answer to Problem 12SGR

Q, R and O are above 50^th percentile.

Explanation of Solution

Given information:

The bowling team scores are,

Bowler	Score
L	112
M	136
N	177
O	65
P	251
Q	74
R	68
S	103

Formula used:

Position of the percentile,

  $=\frac{percentile}{100}\times (n+1)$

Calculation:

Re-arranging the values in an ascending order

Bowler	Score
O	65
R	68
Q	74
S	103
L	112
M	136
N	177
P	251

Substituting the values,

  $=\frac{50}{100}\times (8+1)$

On solving,

  $=4.5$

On rounding off,

  $\approx 5$

Comparing with the graph,

Q, R and O are above 50^th percentile.

b.

To determine

To calculate which bowler is at 38^th percentile

Answer to Problem 12SGR

Q is at 38^th percentile.

Explanation of Solution

Given information:The bowling team scores are,

Bowler	Score
O	65
R	68
Q	74
S	103
L	112
M	136
N	177
P	251

Formula used:

Position of the percentile,

  $=\frac{percentile}{100}\times (n+1)$

Calculation:

Substituting the values,

  $=\frac{38}{100}\times (8+1)$

On solving,

  $=3.42$

On rounding off,

  $\approx 3$

Comparing with the table,

Therefore, Q is at 38^th percentile.