Question

Scores on the the first exam in an introductory statistics course for 12 students.

55, 63, 70, 73, 75, 80, 83, 85, 87, 90, 93, 98

Find the percentile of the score 70

Find the score that corresponds 53 percentile

Find the score that corresponds 60 percentile

Answer 1

(a)

To find the percentile of the score 70:

Sample Size = n = 12

k = Thenumber of values that are less than X = 70 is given by:

k= 2

So,

Percentile Rank (PR) is given by:

PR = 0.1667 12 0.1667 7n

= 16.67 %

o,

Answer is

16.67 %

(b)

To find score corresponding to 53 percentile:

n = 12

Index i is calculated as follows:

53 i=(,-) × n = (-) × 12=6.36 100 100

Since i is not an integer, round up: i = 7

The percentile is at the position i = 7:It is 83.

So,

Answer is:

83

(c)

To find score corresponding to 60 percentile:

n = 12

Index i is calculated as follows:

60 100 100

Since i is not an integer, round up: i = 8

The percentile is at the position i = 8: It is 85.

So,

Answer is:

85