M2LE2 Check Your Understanding Sample Solutions
Instructions: After completing the activity, compare your solutions to the
sample solutions provided. Use the Self-Assessment Rubric (located in the
Rubrics) to assess your own work. Make any necessary adjustments to your
work and be sure to save it for later reference.
1.
Determine whether the following statements are true or false.
a) The higher the percentile rank of a score, the greater the percent of
scores above that score.
False, the percentile rank represents the percent of scores below that
score.
b) A mark of 75% always has a percentile rank of 75.
False, a mark of 75% equals the percentage, percentile rank indicates
how a score compares to other scores. They do not have to be the
same.
c) A mark of 75% might have a percentile rank of 75.
True, often the percentage and the percentile rank are different but in
some cases they can be equal.
d) It is possible to have a mark of 95% and a percentile rank of 40.
True, this indicates that even with a mark of 95%, only 40% scored
lower than this individual or 60% scored higher than this individual.
e)
The higher the percentile rank, the better that score is compared to
other scores.
True, the percentile rank provides information about how an individual
scores in comparison to others.
f)
A percentile rank of 80, indicates that 80% of the scores are above
that score.
False, A percentile rank of 80, indicates that 80% of the scores are
equal to or below that score. OR 20% are above that score.
g) P50 is the median.
True, P50 means that 50% of the scores are equal to or below the score
and 50% of the scores are above. This represents the middle score or
the median.
h) Two equal scores will have the same percentile rank.
True, the same values will be entered into the formula so the percentile
rank will be the same.
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2.
The following is a set of 30 scores achieved by students on an exam:
18
57
81
23
63
82
33
65
85
38
66
89
38
68
92
38
68
93
42
68
93
51
68
95
55
76
97
56
80
100
Determine the percentile rank for each of the following scores.
Remember to round all percentiles to the next whole number.
a) 18
B = 0 (number of scores below 18)
E = 1 (number of scores equal to 18)
N = 30 (total number of scores)
PercentileRank 
B  0.5E
0  0.5(1)
 100 
 100  1.7
n
30
Round up 1.7  2
b) 68
B = 14 (number of scores below 68)
E = 4 (number of scores equal to 68)
N = 30 (total number of scores)
B  0.5E
14  0.5(4)
 100 
 100  53.3
n
30
Round up 53.3  54
PercentileRank 
3.
A total of 700 individuals take a government employment exam.
Carmela scores 618 out of 800 marks. There are 520 individuals who
score less than 618 marks and no one else has a score of 618.
a) Find Carmela’s percent score.
618
 100  77.25%
800
b) Find Carmela’s percentile rank.
B  0.5E
520  0.5(1)
PercentileRank 
 100 
 100  74.4
n
700
Round up to 75.
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c) In order to get a job with the government an individual has be in
the top 20% of people writing the exam. Will Carmela get a job?
Explain.
In order to be considered in the top 20%, Carmela must have a
percentile rank of 80 or greater. With a percentile rank of 75%
Carmela is not quite in the top 20%.
4.
Shana’s final mark in her Grade 12 math class is 92%. Of the 28
students in her class, three received the same grade as Shana and 22
have lower marks.
a) Find Shana’s percentile rank.
B  0.5E
22  0.5(4)
PercentileRank 
 100 
 100  85.7
n
28
Round up to 86.
b) What percentage of students have a final mark higher than Shana?
If Shana has a percentile rank of 86, that means that 86% of the
students have a mark equal to or less than Shana. Therefore, 14% of
the students in the class will have results higher than Shana.
5.
The examination results of 4000 students are analyzed and the following
percentiles are calculated:
P20 = 45
P50 = 61
P75 = 76
P90 = 89
a) Approximately what percentage of students have a score of 45 or
less?
Since P20 = 45, this means that 20% of the students scored 45 or less
on the exam.
b) Approximately what percentage of students have scored more than
76?
Since P75 = 76, then 75% of the students scored 76 or less on the
exam, therefore 25% of the students scored more than 76.
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c) Approximately what percentage of students have scored between 45
and 89?
P20 = 45 and P90 = 89, therefore 70% of the students scored
between 45 and 90. P20 = 45 means that 20% scored 45 or less
and P90 = 89 means that 10% scored more than 89, so that leaves
70% between the two scores.
d) Approximately how many students scored more than 76?
From part (b), 25% scored more than 76. 4000 students wrote the
exam and 25% of 4000 is 1000 students.
e) What is the median mark for this exam?
Since P50 = 61, this is the middle score so the median is 61.
6. Ben has a final overall Grade 12 average of 87%. The college he wants
to attend will not consider any applicant with a percentile rank below 82.
Can Ben be sure the college will consider his application? Explain.
A percentile rank of 82 means that Ben must have a higher average than
18% of the applicants. With an average 87%, Ben might be in the top 18%
but he will not know for sure until his percentile rank is calculated. Having
an average of 87% does not mean his percentile will be higher than 82 for
sure.
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Check Your Understanding Solutions
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