What is the difference between qualitative and quantitative data?

Qualitative is descriptive, quantitative is numerical

In hypothesis testing the p-value represents:

the probability of observing the data if the null hypothesis is true

What is the interquartile range (IQR) of a data set?

the difference between the upper quartile (q3) and the lower quartile (q1)

Which of the following pairs of events are independent?

rolling a die and flipping a coin

In a historgram, the width of the bars represent:

the range of data values within the bin/class

if the median of a data set is 15, which of the following is true?

50% of the data values are less than or equal to 15

What does a negative z-score indicate?

the data point is below the mean

What does the z-score represent in statistics?

the number of standard deviations a data point is from the mean

Which of the following is true about the median?

it is the middle value when data is ordered

What does standard deviation measure?

the spread of data around the mean

if the correlation coefficient(r) between two variables is -0.85, what does this indicate?

a strong negative linear relationship

if two events are mutually exclusive, which of the following is true?

P\left(A∪B\right)=P\left(A\right)+P\left(B\right)

If two events A & B are independent, which of the following must be true?

P\left(A\right|B=P\left(A\right)

If a probability distribution is skewed to the right, what can we infer about the mean?

the mean is greater than the median

the mode of a data set is:

the values that appears most frequently

What is the purpose of a box plot?

to display the distribution of data

Which of the following statements about standard deviation is true?

a smaller standard deviation means the data points are closer to the mean

Which of the following is true for a correlations of -0.9?

the variables are strongly negatively correlated

What does the term 'variance' measure?

the spread of the data points around the mean

What does the area under a probability distribution curve represent?

the total probability, which is always 1

In a box plot, what do the ends of the whiskers represent?

the maximum and minimum data points

a scatter plot shows:

the relationship between two quantitative variables

A probability tree is useful for:

calculating conditional probabilities

If events A and B are independent, which of the following is true?

P\left(A∩B\right)=P\left(A\right)\cdot P\left(B\right)

What is the null hypothesis in a hypothesis test?

a claim that there is no effect or no difference

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IB DP Math - Statistics & Probability Review

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Questions 77

Answers

1
What is the probability of selecting two red marbles in a row from a bag of 3 red & 4 blue marbles, without replacement
\frac{1}{7}
\frac{3}{7}\cdot\frac{1}{7}
\frac{3}{7}\cdot\frac{2}{6}
\frac{2}{7}\cdot\frac{1}{7}
2
What is the difference between qualitative and quantitative data?
Qualitative can be continuous, quantitative cannot
quantitative is subjective, qualitive is objective
Qualitative is descriptive, quantitative is numerical
Qualitative is numerical, quantitative is descriptive
3
Which of the following is NOT a property of a normal distribution
the mean, median, mode are all the same
approximately 68% of data lies within one standard deviation
it has a skewed tail
it is symmetric around the mean
4
If a spinner has 8 equal sections, what is the probability of landing on a section numbered 3 or higher?
\frac{5}{8}
\frac{2}{8}
\frac{1}{8}
\frac{3}{8}
5
In hypothesis testing the p-value represents:
the probability of observing the data if the null hypothesis is true
the probability that the null hypothesis is true
the standard deviation of the sample data
the difference between the sample mean and population mean
6
What is the interquartile range (IQR) of a data set?
the standard deviation of the data
the difference between the upper quartile (q3) and the lower quartile (q1)
the difference between the maximum and minimum value
the mean of the data
7
What is the probability of drawing a red card or a face card from a standard deck of 52 cards?
\frac{26}{52}
\frac{32}{52}
\frac{30}{52}
\frac{28}{52}
8
if a data set has no mode, what does this imply?
there is a negative skew
the mean and median are equal
the standard deviation is 0
all values ae different
9
Which of the following pairs of events are independent?
tossing two coins one after another
drawing two cards from a deck without replacement
rolling a die and flipping a coin
selecting two marbles from a bag without replacement
10
If a data set is normally distributed, how many data points fall within three standard deviations of the mean?
50%
68%
99.7%
95%
11
A data set with two peaks is referred to as
normal
symmetric
bimodal
unimodal
12
In a historgram, the width of the bars represent:
the frequency of data points
the range of data values within the bin/class
the central tendency
the cumulative frequency
13
Which of the following data types can only take on whole number values?
Qualitative
Continuous
Discrete
Quantitative
14
if the median of a data set is 15, which of the following is true?
the mode must be 15
the mean must also be 15
50% of the data values are less than or equal to 15
all data values are 15 or less
15
What does a correlation coefficient of 0.98 suggest?
a weak negative relationship
a weak positive relationship
a strong positive relationship
no relationship
16
What does a negative z-score indicate?
the data point is below the mean
the data point is an outlier
the data point is above the mean
the data point is equal to the mean
17
What does the z-score represent in statistics?
the number of standard deviations a data point is from the mean
the range of a data set
the cumulative frequency of a data point
the average of all data points
18
the shape of the normal distribution is:
bimodal
symmetric and bell-shaped
skewed
asymmetric
19
Which of the following is true about the median?
it is the middle value when data is ordered
it is always affected by outliers
it is the average of all values in the data set
it is always larger than the mean
20
If a coin is flipped 3 times, what is the probability of getting exactly two heads?
\frac{1}{8}
\frac{2}{3}
\frac{3}{8}
\frac{1}{2}
21
What does standard deviation measure?
the spread of data around the mean
the skewness of the data
the difference between the mean and median
the correlation between variables
22
if the correlation coefficient(r) between two variables is -0.85, what does this indicate?
a strong positive linear relationship
no relationship
a weak negative linear relationship
a strong negative linear relationship
23
if two events are mutually exclusive, which of the following is true?
P\left(A∩B\right)=P\left(A\right)+P\left(B\right)
P\left(A∪B\right)=P\left(A\right)\cdot P\left(B\right)
P\left(\left(A∩B\right)\right)=P\left(A\right)\cdot P\left(B\right)
P\left(A∪B\right)=P\left(A\right)+P\left(B\right)
24
If two events A & B are independent, which of the following must be true?
P\left(A\right|B=P\left(A\right)
P(A|B) = 0
P\left(A∩B\right)=0
P\left(A∪B\right)=P\left(A\right)\cdot P\left(B\right)
25
If a probability distribution is skewed to the right, what can we infer about the mean?
the mean is less than the median
the mean and median are equal
the mean is greater than the median
the mode is greater than the mean
26
if the residuals from a regression model show no pattern, what does this indicate?
a perfect fit
multicollinearity
a random error distribution
a poor fit
27
What is the sum of probabilities of all possible outcomes in a probability experiment?
0
1
infinity
0.5
28
if the probability of rain is 0.7, what is the probability that it will not rain?
1.0
0.3
0.7
0.5
29
The probability of event A=0.3. The prob. of event B=0.5. What is the prob. that both events occur, assume independence
0.5
0.2
0.15
0.8
30
the mode of a data set is:
the average of all values
the middle value when the data set is ordered
the difference between the highest and lowest values
the values that appears most frequently
31
In a cumulative frequency graph, the vertical axis represents:
class interval
cumulative frequency
frequency
relative frequency
32
What is the purpose of a box plot?
to display the distribution of data
to show the relationship between two variables
to display frequency of data points
to calculate the mean
33
What is the probability of getting at least one head in two flips of a fair coin?
\frac{3}{4}
\frac{1}{4}
\frac{1}{8}
\frac{1}{2}
34
Which of the following statements about standard deviation is true?
a larger standard deviation means the data points are closer to the mean
a smaller standard deviation means the data points are spread out
a smaller standard deviation means the data points are closer to the mean
a larger standard deviation means the data points are closer to the mean
35
What is the probability of drawing two aces in a row from a standard deck of 52 cards, without replacement?
\frac{1}{13}
\frac{4}{52}\cdot\frac{3}{51}
\frac{1}{26}
\frac{1}{169}
36
What is the probability of rolling a 3 or a 5 on a single roll of a die?
\frac{1}{6}
\frac{1}{3}
\frac{1}{2}
\frac{2}{6}
37
What is the probability of not drawing an ace from a deck of 52 cards?
\frac{48}{52}
\frac{1}{4}
\frac{2}{3}
\frac{4}{52}
38
Which of the following is true for a correlations of -0.9?
the relationship is nonlinear
the variables are weakly correlated
the variables are strongly negatively correlated
there is no correlation
39
What does the term 'variance' measure?
the average of data points
the spread of the data points around the mean
the difference between the maximum and minimum values
the relationship between two variables
40
What is the probability of rolling a 6 on two consecutive rolls of a fair die?
\frac{1}{12}
\frac{1}{6}
\frac{1}{18}
\frac{1}{36}
41
Which graph is best suited for displaying the distribution of a single variable?
Bar Chart
Scatter Plot
Pie Chart
Histogram
42
In a symmetric distribution, how do the mean, median, and mode compare?
the mean is larger than the median and mode
the mode is larger than the mean and median
the median is smaller than the mean and mode
They are all equal
43
What does the area under a probability distribution curve represent?
the total probability, which is always 1
the variance of the data set
the range of data values
the mean of the distribution
44
In a box plot, what do the ends of the whiskers represent?
the maximum and minimum data points
the interquartile range
the first and third quartiles
the mean and median
45
a scatter plot shows:
the frequency of categorical data
the cumulative frequency of data points
the distribution of a single variable
the relationship between two quantitative variables
46
A probability tree is useful for:
calculating conditional probabilities
calculating the mean
visualizing mutually exclusive events
visualizing independent events
47
What does it mean if the standard deviation of a data set is 0?
the mean is 0
all data points are identical
the median is 0
the data set is highly variable
48
If the probability of event A is 0.4 and the probability of event B is 0.3, what is P(AUB) if A & B are independent?
0.58
0.5
0.7
0.12
49
Which of the following is a discrete data set?
number of students in a class
height of students
Time spent studying for exams
amount of water in a bottle
50
If events A and B are independent, which of the following is true?
\left(P\left(A\right|B\right)=P\left(A\right)
P\left(A∩B\right)=P\left(A\right)\cdot P\left(B\right)
P\left(A∩B\right)=P\left(A\right)+P\left(B\right)
P\left(A∪B\right)=P\left(A\right)+P\left(B\right)
51
What is the null hypothesis in a hypothesis test?
a claim that there is no effect or no difference
a claim that the mean is greater than 0
a claim that there is significant effect
a claim that the sample data are incorrect
52
If the correlation between two variables is close to zero, what can be inferred?
there is a strong positive relationship
there is no linear relationship between the variables
the variables are highly correlated
the relationship is nonlinear
53
A class of 20 scholars, has 12 boys & 8 girls. A student is selected randomly,what is the probability that it is a girl?
\frac{12}{20}
\frac{1}{4}
\frac{1}{2}
\frac{8}{20}
54
the probability of rolling a prime number on a six-sided die is:
\frac{1}{6}
\frac{1}{2}
\frac{2}{3}
\frac{1}{3}
55
If the mean of a data set is 50 and the standard deviation is 10, what is the z-score of a data point at 70?
-2
1
2
0
56
a bimodal distribution indicates:
a negatively skewed distribution
a data set with no variation
a symmetric distribution
a data set with two peaks
57
What is the probability of rolling a sum of 7 with two dice?
\frac{5}{36}
\frac{6}{36}
\frac{1}{36}
\frac{7}{36}
58
Which type of graph is best suited for displaying the relative frequency of categorical data?
box plot
bar chart
scatter plot
histogram
59
What is the probability of flipping 3 heads in a row with a fair coin?
\frac{1}{4}
\frac{3}{8}
\frac{1}{2}
\frac{1}{8}
60
What does a box in a box plot represent?
the range of the data
the mean of the data
the mode of the data
the interquartile range
61
Which of the following is not a measure of central tendency?
mode
mean
range
median
62
In a probability experiment, which of the following is true for mutually exclusive events?
\left(P\left(A\right|B\right)=P\left(A\right)
P\left(A∪B\right)=1
P\left(A∩B\right)=0
P\left(A∪B\right)=P\left(A\right)\cdot P\left(B\right)
63
If the IQR of a data set is 12, what does this tell you about the data?
the range of the data is 12
the middle 50% of the data is spread out over a range of 12
there are 12 data points
the data is skewed to the right
64
What does the slope of a least-squares regression line represent?
the strength of the relationship between variables
the correlation between two variables
predicted change in dependent variable as independent variable increases
the total variation in the data
65
A bag contains 3 red, 4 green, and 5 blue marbles. What is the probability of selecting a red marble?
\frac{1}{12}
\frac{1}{4}
\frac{1}{3}
\frac{3}{12}
66
What is the expected value of a roll of a fair six-sided die?
4
3.5
3
2.5
67
The probability of event A is 0.6 & of event B is 0.4. The events are mutually exclusive, what is P\left(A∪B\right)
0.4
0.24
1
0.6
68
Which measure of central tendency is most affected by extreme values?
Mean
Median
Range
Mode
69
What is the effect of an outlier on the mean?
the mean will decrease
the mean may increase or decrease, depending on the outlier
the mean will increase
the mean will remain unchanged
70
What is the probability of drawing an ace from a standard deck of 52 cards?
\frac{1}{13}
\frac{1}{52}
\frac{1}{4}
\frac{4}{52}
71
If a dataset has a negative skew, which of the following is true?
the mean and median are equal
the standard deviation is zero
the mean is greater than the median
the mean is less than the median
72
Which of the following would likely result in a negative correlation?
hours spent studying and exam scores
distance traveled and fuel consumption
number of hours worked and amount of money earned
hours of exercise and weight loss
73
In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
50%
95%
68%
99.7%
74
In a positively skewed distribution, which of the following is true?
the mean is greater than the median
the median is greater than the mean
the mode is greater than the mean
the mean is less than the median
75
the range of a data set is defined as:
the most frequent data point
the average of all data points
the difference b etween the maximum and minimum values
the middle value when the data is ordered
76
What is a residual in a regression analysis?
the slope of the regression line
the average of the independent variable
the correlation between the two variables
the difference between the observed and predicted values
77
a sample mean is:
the average of the population
the average of the sample data
the mode of the sample data
the median of the sample data

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