Question

Percentile rank. Describe in c) Construct a ten-score dataset such words what it means for a score to of 92 falls into the 70h Percentile. Use the oue be in %ile Rank =1 B+ 호 E |.100% a) the 85th Percentile. h) the 16th Percentile.

Answer 1

(a) In an ascending orderd sores of n terms (counts), a score k is said to be in 85th percentile if k is the term existed at the position (rank): 85x(n+1)/100. It means that the scores less than or equal to the score k are of 85% of total count of all scores and the scores more than the score k are of 15% of total count of all scores.

(b) In an ascending orderd sores of n terms (counts), a score p is said to be in 16th percentile if p is the term existed at the position (rank): 16x(n+1)/100. It means that the scores less than or equal to the score p are of 16% of total count of all scores and the scores more than the score p are of 84% of total count of all scores.

(c) Suppose some 10 scores are arranged in ascending order in 10 positions as follws:   

Position	1	2	3	4	5	6	7	8	9	10
Score	52	52	61	65	70	80	92	92	98	99

Now, the score at the 70th percetile is the score at the position (rank):70x(n+1)/100

position (rank):70x(n+1)/100 = 70x(10+1)/100 = 7.7

=7th position score + 0.7x(8th position score -7th position score)

=92+0.7x(92 - 92)

=92+0.7x(0)

=92+0

=92

Therefore a ten-score data set such that a score of 92 falls in the 70th percentile is

{52, 52, 61, 65, 70, 80, 92, 92, 98, 99}

From the above data the percentile rank for the score 92 = ((B+(E/2))/n)x100%

where, B is the number of counts of scores below 92 = 6

E is the number of counts of score 92 = 2 and here n=10

Hence, the percentile rank for the score 92 = ((6+(2/2))/10)x100% = ((6+1)/10)x100% = (7/10)x100% =(0.7)x100% = 70%

(OR)

In the similar way, another type of data may be generated as follows if some scores are in fractions:

Suppose some 10 scores are arranged in ascending order in 10 positions as follws:   

Position	1	2	3	4	5	6	7	8	9	10
Score	52	52.5	61	65.5	70	80.5	88.5	93.5	98.5	99

Now, the score at the 70th percetile is the score at the position (rank):70x(n+1)/100

position (rank):70x(n+1)/100 = 70x(10+1)/100 = 7.7

=7th position score + 0.7x(8th position score -7th position score)

=88.5+0.7x(93.5 -88.5)

=88.5+0.7x(5)

=88.5+3.5

=92

Therefore a ten-score data set such that a score of 92 falls in the 70th percentile is

{52, 52.5, 61, 65.5, 70, 80.5, 88.5, 93.5, 98.5, 99}

From the above data the percentile rank for the score 92 = ((B+(E/2))/n)x100%

where, B is the number of counts of scores below 92 = 7

E is the number of counts of score 92 = 0 and here n=10

Hence, the percentile rank for the score 92 = ((7+(0/2))/10)x100% = ((7+0)/10)x100% = (7/10)x100% =(0.7)x100% = 70%