# The following frequency distribution presents a set of exam scores for a class of N = 20 students...X         f    cf    c% 90-99  4   20   100 80-89  7   16   80 70-79  4    9  ...

The following frequency distribution presents a set of exam scores for a class of N = 20 students...

X         f    cf    c%

90-99  4   20   100

80-89  7   16   80

70-79  4    9    45

60-69  3    5    25

50-59  2    2    10

Find the 30th percentile? What is the percentile rank for X = 72 and 90?

lambert86 | Student, Undergraduate | (Level 2) eNoter

Posted on

According to the data given the 30th percentile lies in the group 70-79.

The lower boundry of that class= 69.5

Upper boundry= 79.5

If 30th percentile = P30,

(P30-P25)/(P45-P25)=(F30-F25)/(F45-F25)

Where,

P30,P25,P45- 30th, 25th and 45th percentiles respectively, and

F30,F25,F45- Cumulative frequencies for 30th, 25th and 45th percentiles respectively.

From the given data;

P25= 69.5

P45=79.5

F25= 5

F45= 9

F30= 30*20/100= 20

By subsitituting values:

(P30-69.5)/(79.5-69.5)=(6-5)/(9-5)

P30= 69.5 + 10*1/4

= 69.5 + 2.5

P30= 72

Since P30=72; Percentile for X=72 is 30th.

To find the percentile for x=92

x=92 is in the percentile range of 80-100.

Assume the percentile relevant to x=92 as Z.

Therefore,

(92-89.5)/(99.5-89.5)=(Z-80)/(100-80)

(2.5)/(10)=(Z-80)/(20)

Z= 80 + (2.5)(20)/(10)

z= 80 + 5 = 85

Therefore percentile rank for 92 = 85