# 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?

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### 1 Answer

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**