# Given the following data, find the 30th percentile?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...

Given the following data, find the 30th percentile?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

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### 1 Answer

You should find the 30th percentile, hence, you need to locate it between`25%` and `45%` . Now, you need to look for the scores that correspond to these percentages such that:

`c% = 25% =gt X = 60-69 `

`c% = 45% =gt X = 70-79 `

You need to find the length of the interval between `25%` and `45%` such that:

`45 - 25 = 20`

As a fraction, 30th percentile is located `30/45 = 6/9 = 2/3` down from the top of interval.

You need to find the X value that is located `1/3` down from the top of interval. The top of X interval is`53.5` and the bottom value is `52.5,` hence, the length of interval is `53.5 - 52.5 = 1` .

The position you look for is `2/3` down from the top of interval such that:

`(2/3)*1 = 2/3 = 0.6`

You need to find the position subtracting `0.6` from `53.5` such that:

`53.5 -0.6 = 52.83`

**Hence, evaluating the 30th percentile under the given conditions yields X = 52.83.**