Chapter 2 - Measures of Center, Variability, Z-score, & Quartiles
Chapter 2 - Tchebysheff’s Theorem & Empirical Rule
Chapter 3 - Covariance, Correlation Coefficient, & Regression Line
Chapter 4 - Basic Probability Theory, mn Rule, Permutations, Combinations
Chapter 4 - Event Relations
100
Consider a sample {4, 6, 2, 3, 2}
Find the mean, median, mode, and range
Double points: which measure of center is most affected by extreme values?
Mean = 3.4
Median = 3
Mode = 2
Range = 4
Mean
100
Draw a mound-shaped graph and label the percentage distributions between 1, 2, and 3 standard deviations from the mean.
Double points: what is this method called?
68%, 95%, 99%
Empirical rule
100
Draw a scatterplot for the following correlations: strong negative, perfect positive, and no relationship.
100
Toss a fair coin 3 times. What is the probability of observing at least two tails?
1/2
100
Toss a coin twice: S = {HH, HT, TH, TT}
Event A: at least one head
Event B: exactly one tail
What is A complement, A intersect B, A union B?
A complement = {TT}
A intersect B = {HT, TH}
A U B = {HH, HT, TH}
200
Consider a sample {3, 1, 5, 2, 4}
Find the sample variance and standard deviation
Variance = 2.5
Standard deviation = 1.58
200
Using Tchebysheff’s Theorem, what is the percentage of measurement that will lie within 1, 2, and 3 standard deviations?
0, 75%, 89%
200
What is the strength and direction for the following values?
r = -0.1
r = 0.6
r = 0
r = -0.1: weak negative linear relationship
r = 0.6: strong positive linear relationship
r = 0: no relationship
200
Are these mutually exclusive - rolling multiples of 2 and rolling multiples of 3 on dice?
No
A = {2, 4, 6}
B = {3, 6}
200
At a college, 65% of students took a stats class, 45% took a business class, and 20% of students took both.
What is the percentage of students who have taken neither?
10%
300
Consider a sample {2, 8, 4, 3, 6} and given s = 2.41
Compute the z-score of 8
Is the score not unusual, somewhat unusual, or an outlier?
Z-score = 1.41
The score is not unusual
300
Suppose the average test score for an exam is 75 with the standard deviation of 10.
Suppose we know the distribution of the test scores is mound-shaped, what is the proportion of scores between 65 and 85?
Approximately 68%
300
The following is given: x = {2, 4, 5, 3, 3, 1}, Σx = 18, Σy = 241, and Σxy = 844
Calculate the covariance
24.2
300
Three M&Ms are drawn one by one in order from a dish containing 6 candies. The total number of simple events is:
120
300
Given that the student is female, what is the probability that she is colorblind?
2/490
400
Label the five-number-summary of this box plot
Double points: give the percentages of data within each section
Minimum/lowest value, lower quartile, median, upper quartile, maximum/highest value
25% between each label
400
Suppose the average test score for an exam is 75 with the standard deviation of 10.
Suppose we do not know the distribution of the test scores, what is the proportion of scores between 55 and 95?
At least 75%
400
The basic statistics are calculated: sᵪ2 = 3.5, sᵧ2 = 3195.2, and sᵪᵧ = 103.8
Find the correlation coefficient
Indicate the relationship between x and y
0.98
Strong positive relationship
400
Three members of a 5-person committee must be chosen to form a subcommittee. How many different subcommittees could be formed?
10
400
Toss a fair coin twice. Define:
A: head on second toss
A complement: tail on second toss
B: head on the first toss
B complement: tail on the first toss
If B occurred, what is the probability that A occurred?
If B didn't occur, what is the probability that A occurred?
Are A and B independent?
1/2
1/2
Yes because the probabilities are the same
500
Given the five-number-summary of a dataset: 35, 48, 58, 63, 85
What is the percentage of measurements that lie in the inter-quartile-range (from 48 to 63)
What is the percentage that lie between 35 and 63?
50%
75%
500
Suppose the average test score for an exam is 75 with a standard deviation of 10.
Suppose we know the distribution of the test scores is mound-shaped, what is the proportion of scores between 55 and 85?
Approximately 81.5%
500
The basic statistics are calculated: x̄ = 2.83, ȳ = 37.5, sᵪ = 1.47, sᵧ = 15.41, and r = 0.9
Find the best fitting regression line
Predict for a family of 5
y = 10.81 + 9.43x
y(5) = 57.96
500
How many 4-digit lock passwords can we make by using 4 different numbers from 0 to 9?
5040
500
Suppose 49% of the adult population in a state are female (F).
Also, of the females, 35% have a college degree (C).
A single person is selected at random from the population. What is the probability that the person is a female with a college degree?
.1715