Question

The table below shows the distribution of scores in a Statistics test given to a class of 40 students. The teacher decided to pass the upper 40% of these students

Class Limits f

91-97 2
84-90 3
77-83 7
70-76 15
63-69 6
56-62 4
49-55 3


1. What is the passing score?
2. What is the percentile rank of the student hwhose score is 80?

Answer 1

Answer on Question #44748 – Math - Statistics and Probability

The table below shows the distribution of scores in a Statistics test given to a class of 40 students. The teacher decided to pass the upper 40% of these students

1. What is the passing score?

2. What is the percentile rank of the student whose score is 80?

Solution

1. The passing score is 40th percentile.

kth percentile is

$$\mathrm{kth\ percentile} = \mathrm{L} + \frac{\frac{kN}{100} - cf}{f} \cdot w$$

where $L$ is lower limit of $P_{k}$ class, $f$ is frequency of $P_{k}$ class, $cf$ is cumulative frequency of the class just preceding $P_{k}$ class, $w$ is size of $P_{k}$ class, $N$ is total numbers of items.

In this example (40th percentile class is 70-76):

$$L = 70, f = 15, N = 40, cf = 12, w = 7.$$ $$40\text{th percentile} = 70 + \frac{\frac{40 \cdot 40}{100} - 12}{15} \cdot 7 = 71.87.$$

2. What is the percentile rank of the student whose score is 80?

$$80 = 77 + \frac{\frac{k \cdot 40}{100} - 5}{7} \cdot 7 \rightarrow k = 20.$$

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