Question

1. Suppose in a class of 100 students who took an exam scored out of 100, the 68thpercentile of the exam scores was 72. Thus, _________% of the students who took the exam scored less than a 72.

a.32%

b.68%

c.72%

d.28%

e.None of the above

2. Suppose in a class of 80 students who took an exam scored out of 100, the 40thpercentile of the exam scores was 58. Approximately how many of the 80 students scored above a 58?

a.32

b.68

c.72

d.48

e.None of the above

Explain, please.

Answer 1

1.

A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls. For example, the 20th percentile is the value below which 20% of the observations may be found.

Since we are given that 68^th percentile of the exam scores was 72

So, 68 % of the student scores lie below 72

Hence, 68% of the students who took the exam scored less than a 72.

Correct option : b. 68%

2.

We are given that 40^th percentile of the exam scores was 58

So, 40% of the student scores lie below 58

This implies that 60% of the student scores lie above 58

Now, there are in total 80 students

So,

60% of 80 = 0.60*80 = 48

Correct option : d. 48