Math 3339 Test 1 Review Updated Exam 2026
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percentile - ANSWERS-A point on a ranking scale of 0 to 100. The 50th percentile is the
midpoint; half the people in the population being studied rank higher and half rank
lower.
in a collection of 30 data measurements, which measurement represents the 25th
percentile? - ANSWERS-n = 30
P = 0.25
rank = nP+0.5 = 8
8th measurement = 25th percentile
find which number is at a certain percentile - ANSWERS-1) %-tile = nP+0.5
2a) if decimal of %-tile != 0.5, choose round rank. EX: if 10th %-tile = 19.25 -> 19th
element is 10th percentile
2b) if decimal of rank = 0.5, take average. EX: if 10th %-tile = 19.5 -> get average of
19th and 20th element.
R command: 5 number summary - ANSWERS-fivenum(listname)
R command: find value of 95th percentile in list - ANSWERS-quantile(listname, 0.95)
R command: stem plot - ANSWERS-stem(listname, scale=(optional # from 0 to 1))
, sample variance formula - ANSWERS-R command: sd()
coefficient of variation formula - ANSWERS-greater cv -> greater variability
covariance - ANSWERS-A measure of linear association between two variables.
Positive values indicate a positive relationship; negative values indicate a negative
relationship
correlation - ANSWERS-A measure of the extent to which two factors vary together, and
thus of how well either factor predicts the other.
Chebyshev's Inequality - ANSWERS-The percentage of the observations that lie within
k standard deviations of the mean is at least 1 - (1/k^2) when k > 1
binomial distribution - ANSWERS-Fixed probability; given number of trials; only 2
possible outcomes
mean for binomial distribution - ANSWERS-μ = np
standard deviation for binomial distribution - ANSWERS-σ = √(np(1-p))
R command: For binomial distribution, n=50 and p=0.4, find P(X <= 5). - ANSWERS-
pbinom(5, 50, .4)
R command: For binomial distribution, n=50 and p=0.4, find P(X = 5). - ANSWERS-
dbinom(5, 50, .4)
hypergeometric distribution - ANSWERS-from two types of items (A and B); select some
fixed number; count how many of A you get
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Exam Questions (Actual Exam 2026-2027)
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percentile - ANSWERS-A point on a ranking scale of 0 to 100. The 50th percentile is the
midpoint; half the people in the population being studied rank higher and half rank
lower.
in a collection of 30 data measurements, which measurement represents the 25th
percentile? - ANSWERS-n = 30
P = 0.25
rank = nP+0.5 = 8
8th measurement = 25th percentile
find which number is at a certain percentile - ANSWERS-1) %-tile = nP+0.5
2a) if decimal of %-tile != 0.5, choose round rank. EX: if 10th %-tile = 19.25 -> 19th
element is 10th percentile
2b) if decimal of rank = 0.5, take average. EX: if 10th %-tile = 19.5 -> get average of
19th and 20th element.
R command: 5 number summary - ANSWERS-fivenum(listname)
R command: find value of 95th percentile in list - ANSWERS-quantile(listname, 0.95)
R command: stem plot - ANSWERS-stem(listname, scale=(optional # from 0 to 1))
, sample variance formula - ANSWERS-R command: sd()
coefficient of variation formula - ANSWERS-greater cv -> greater variability
covariance - ANSWERS-A measure of linear association between two variables.
Positive values indicate a positive relationship; negative values indicate a negative
relationship
correlation - ANSWERS-A measure of the extent to which two factors vary together, and
thus of how well either factor predicts the other.
Chebyshev's Inequality - ANSWERS-The percentage of the observations that lie within
k standard deviations of the mean is at least 1 - (1/k^2) when k > 1
binomial distribution - ANSWERS-Fixed probability; given number of trials; only 2
possible outcomes
mean for binomial distribution - ANSWERS-μ = np
standard deviation for binomial distribution - ANSWERS-σ = √(np(1-p))
R command: For binomial distribution, n=50 and p=0.4, find P(X <= 5). - ANSWERS-
pbinom(5, 50, .4)
R command: For binomial distribution, n=50 and p=0.4, find P(X = 5). - ANSWERS-
dbinom(5, 50, .4)
hypergeometric distribution - ANSWERS-from two types of items (A and B); select some
fixed number; count how many of A you get
