Statistics & Probability MCQs
Statistics & Probability MCQs
These Statistics & Probability multiple-choice questions and their answers will help you strengthen your grip on the subject of Statistics & Probability. You can prepare for an upcoming exam or job interview with these Statistics & Probability MCQs.
So scroll down and start answering.
1: What is the median of: 5, 10, 15?
A. 9.5
B. 15
C. 5
D. 10
2: What is the mean of a standard normal distribution?
A. 0
B. 0.5
C. 100
D. 1
E. 50
3: What is true about these 5 numbers? -2, -1, 0, 5, 10
A. The mean is larger than the median.
B. The median is larger than the mean.
C. Cannot compare means and medians.
D. The median and mean are equal to each other.
4: If a data set follows a normal distribution, approximately ___% of data falls within 1 standard deviation of the mean.
A. 68%
B. 0%
C. 25%
D. 100%
5: The number of cars that went through a car wash during the noon hour over each of the past 8 days are the following: 5, 9, 2, 3, 3, 9, 8, 6 What is the range of this data?
A. 7
B. 9
C. 5.6
D. 8
6: You flip an unbiased coin 2 times - what is the probability of getting 2 heads?
A. 50%
B. Cannot determine
C. 100%
D. 75%
E. 25%
7: Discrete and continuous data are both forms of _______ data.
A. incomplete
B. qualitative
C. quantitative
D. None of these
8: What is the average of the following 5 numbers? 1, 2, 3, 4, 10
A. 1
B. 10
C. 4
D. 3
9: What is the mode of: 5, 10, 10, 15, 17?
A. 12
B. 5
C. 10
D. 11.2
10: What is the value of the middle observation in a ordered set of numbers
A. Median
B. Mode
C. Central Standard
D. Mean
11: The ______ describes the dispersion of a data set.
A. standard deviation
B. median
C. None of these
D. mean
12: Which of the following is quantitative data:
A. A schedule of meetings
B. Test scores for English class
C. A list of song titles
D. A prescription written by a physician
13: A mean calculation is a part of _______ statistics.
A. non-parametric
B. Neither of these
C. parametric
14: Where would the outliers be if a distribution had a skewness of 0?
A. Left
B. No outliers
C. Far right
D. Right
E. Far left
15: You flip an unbiased coin one time - what is the probability of getting tails?
A. 50%
B. 25%
C. Cannot determine
D. 75%
E. 100%
16: The difference between the highest and lowest scores is called the ______.
A. range
B. mean
C. sample
D. mode
17: The Square of the standard deviation is called
A. Covariance
B. Variance
C. Mean
D. Squared Distribution
18: What is the mean of: 5, 10, 15?
A. 11
B. 1
C. 10
D. 5
19: A normal distribution generally takes the form of _______.
A. square ruit
B. bell curve
C. None of these
D. asymptote
20: What is the median of the following 5 numbers? 1, 2, 3, 4, 10
A. 4
B. 3
C. 1
D. 10
21: True or false? Qualitative data is strictly numerical.
A. False
B. True
22: What power is used in the formula for variance?
A. 4
B. 3
C. 5
D. 1
E. 2
23: What is the skewness of a normal distribution?
A. 3
B. 4
C. 2
D. 0
E. 1
24: The average grade on a midterm exam in a math class is 72. The teacher feels this is too low, so they award 10 extra points to every student in the class. What is the new average grade for the class?
A. Not enough information.
B. 62
C. 82
D. 72
25: Two coins are tossed, what is the probability that two heads are obtained?
A. .75
B. .5
C. .25
D. 0
E. .125
26: The, "null hypothesis," refers to
A. That the relationship depends on other factors
B. That there is a minor relationship between two phenomena
C. That there is a significant relationship between two phenomena
D. that there is no relationship between two phenomena
27: Your college professor standardizes everyone's test scores. Your standardized score is -1.35. Which of the following statements is true?
A. You scored within one standard deviation of the average test score.
B. Your test score was above the average.
C. Your test score was below the average.
D. Your test score had the highest standard deviation.
28: The median grade on a midterm exam in a math class is 72. The teacher feels this is too low, so they award 10 extra points to every student in the class. What is the new median grade for the class?
A. 62
B. 82
C. Not enough information.
D. 72
29: Which of the following is a measure of spread?
A. Mean
B. Lower Quartile
C. Median
D. Range
30: Which of the following is NOT a characteristic of a Normal distribution?
A. Defined completely by mean and variance
B. Unimodal
C. Right Skewed
D. Symmetric
31: Let A be a normal distribution with a mean of 3 and B be a normal distribution with a mean of 17. What is the mean of A+B?
A. 14
B. 3
C. 17
D. 20
E. 51
32: A forestry researcher recorded many variables on the trees of a large forest. These variables include the height (in meters), the diameter (in centimeters), the species (pine, oak, etc.), and if the tree had Dutch Elm disease. In this study which variables that were recorded were quantitative?
A. Only species and height.
B. Only height.
C. Only height and diameter.
D. All of the variables.
33: How can you convert a variance to a standard deviation?
A. Variance = standard deviation
B. Take the square root of the variance
C. Take the cubed root of the variance
D. Take the log of the variance
E. Square the variance
34: Using previous games to predict the score of a game is an example of ________ statistics.
A. inferential
B. descriptive
C. incomplete
D. None of these
35: Bob is a high school basketball player, who is a 72% free throw shooter. Bob has missed his first four free throws of the game. What is the probability that Bob makes his fifth free throw?
A. 0%
B. 72%
C. 90%
D. 100%
36: Where would the outliers be if a distribution had a skewness of -50?
A. Far left
B. Left
C. Right
D. Far right
E. No outliers
37: Over the last 360 days of winter in Raleigh, NC (5 winters) we have had snow on 36 days. What is the probability that we will have snow on any random winter day this year?
A. 0.05
B. 0.1
C. 0.01
D. 0.2
38: Which of the following is not a measure of spread?
A. Variance
B. Range
C. Upper Quartile
D. Standard Deviation
39: What is the probability of rolling a fair dice and getting an even number?
A. 1/2
B. 4/6
C. 1/6
D. 1/3
40: You calculate the standard deviation of a data set and find that it is -1.23. From this you can determine which of the following is true?
A. The mean must be negative.
B. You made an arithmetic mistake because standard deviation cannot be negative.
C. Every value in the data set is the same.
D. All of the values in the data set are negative.
41: Where would the outliers be if a distribution had a skewness of +1?
A. Right
B. Left
C. Far right
D. No outliers
E. Far left
42: Suppose E is an event in a sample space S with probability .3. What is the probability of the complement of E?
A. .3
B. .7
C. 1
D. 0
43: What is true about these 5 numbers? -10, -5, 0, 1, 2
A. Cannot compare means and medians.
B. The median and mean are equal to each other.
C. The median is larger than the mean.
D. The mean is larger than the median.
44: How is P(A|B) interpreted?
A. The probability that event A or event B happens
B. The probability event A happens given that event B has happened
C. The probability event A happens given that event B did not happen
D. The probability event B happens given that event A has happened
45: Symbolism: What does the small sigma represent (without any other symbols) in statistics?
A. Mean
B. Skewness
C. Expected Value
D. Standard Deviation
E. Variance
46: _____ are collections of observations.
A. Random variables
B. Data
C. Expected values
D. Populations
47: What is the difference between the mean and the median?
A. Median is not affected by skewness of the distribution
B. Both are always equal
C. Mean is always greater than the Median
D. Mean is not effected by skewness of the distribution
48: Where would the outliers be if a distribution had a skewness of +50?
A. No outliers
B. Right
C. Left
D. Far left
E. Far right
49: A ______ is a numerical characteristic of a population
A. None of these
B. category
C. parameter
D. constraint
50: What is the probability of rolling a fair dice and getting a 1 and flipping a fair coin getting a head?
A. 1/12
B. 1/6
C. 3/12
D. 1/2
51: Suppose a fair die is tossed twice. What is the probability of rolling two fours?
A. 1/6/2013
B. 2/36
C. 1/36
D. 2/6/2013
52: What is expected value?
A. The probability of the next outcome
B. No such thing
C. All of the other choices, beside "no such thing"
D. Sum of all the possible outcomes * the probability of occurrence
E. The maximum loss
53: How do you calculate the Z-Score?
A. = observation + standard deviation
B. = (observation - sample mean) / standard deviation
C. = standard error of the mean / standard deviation
D. = observation + standard deviation / standard error of the mean
E. = observation - standard deviation
54: Symbolism: What does the x-bar represent (without any other symbols) in statistics?
A. Population mean
B. Sample standard deviation
C. None of the other options
D. Sample mean
E. Population standard deviation
55: Which plot is best use to display the relationship between a continuous dependent variable against a continuous independent variable
A. Scatter plot
B. Box Plot
C. Bar Chart
D. None of these
E. Histogram
56: How can you convert a standard deviation to a variance?
A. Take the cubed root of the standard deviation
B. Square the standard deviation
C. Take the square root of the standard deviation
D. Variance = standard deviation
E. Take the log of the standard deviation
57: The variable X is the value of an uneven dice after one roll. It produced the following probability distribution P(X): P(1) = 0.05 P(2) = 0.28 P(3) = 0.12 P(4) = 0.23 P(5) = ? P(6) = ? What is the probability that X = 5 or X = 6?
A. 0.42
B. 0.23
C. 0.55
D. 0.32
58: The variable X is the value of an uneven dice after one roll. It produced the following probability distribution P(X): P(1) = 0.05 P(2) = 0.28 P(3) = 0.12 P(4) = 0.23 P(5) = ? P(6) = ? What is the probability that X = 2 or X = 3?
A. 0.28
B. 0.45
C. 0.4
D. 0.12
59: The average price of a car in a used car lot is $18,000. These prices are Normally distributed with a standard deviation of $3,000. What is the probability that any random car is below $18,000?
A. 68%
B. 50%
C. 95%
D. 42%
60: What is the probability of rolling a fair dice and getting an even number and flipping a fair coin getting a head?
A. 0.25
B. 0.75
C. 0.5
D. 0
61: Which of the following is an example of mutually exclusive events?
A. Having it rain on the same day that the sun comes out in the same city
B. Ordering a burger at a fast food restaurant and ordering fries at that same restaurant
C. Having one product off the assembly line be defective, but another product on that same assembly line work properly.
D. Being late to a meeting and being early to the same meeting
62: Interpret an R-squared coefficient of .6 for a simple linear regression.
A. There is no interpretation for the R-squared value.
B. 60% of the variability in our dependent variable can be explained by our independent variable.
C. This is an indicator that there must be a moderate positive correlation between both the dependent and independent variables.
D. We can be 60% certain that there is a causal relationship between our dependent and independent variables.
63: What is the most commonly used statistical measure of spread in a normally-distributed population?
A. mean
B. variance
C. standard deviation
D. covariance
E. z-score
64: When does a Type I error occur?
A. None of the other choices
B. All of the other choices
C. You reject the null hypothesis when it is true
D. There is no such term as a "Type I Error"
E. You fail to reject the null hypothesis when it is false
65: In a probability distribution, the second central moment can be another term for which of the following?
A. Skewness
B. Average
C. Kurtosis
D. Variance
66: What is derived from the second moment of distribution?
A. Mean
B. Skewness
C. Pearson's Coefficient of Kurtosis
D. Variance
E. Kurtosis
67: Experts rank athletic teams 1 through 10. This is an example of ______ data.
A. discrete
B. categorical
C. quantative
D. ordinal
68: Which one of these variables is a continuous random variable?
A. The time it takes a randomly selected student to complete an exam.
B. The number of tattoos a randomly selected person has.
C. The number of women taller than 68 inches in a random sample of 5 women.
D. The number of correct guesses on a multiple choice test.
69: What is the median of the following 5 numbers? 10, 2, 4, 3, 1
A. 3
B. 4
C. 1
D. 10
70: Suppose E and F are mutually exclusive events in a sample space S with probabilities .4 and .3 respectively. What is the probability of their union?
A. .4
B. .1
C. .3
D. .7
71: The probability of a discrete value in a continuous distribution is equal to __?
A. -1
B. .99
C. 1
D. 0
E. 0.5
72: Suppose c is a constant number. Calculate var(c).
A. c^2
B. c
C. 0
D. c^2 - c
E. c^2+c
73: What is the first moment of distribution?
A. Mean
B. Standard Deviation
C. Skewness
D. Variance
E. Kurtosis
74: _____ data is an example of nonmetric data.
A. Quantative
B. Ordinal
C. Sample
D. Parametric
75: Which of the following statements are true? 1. Categorical variables are the same as qualitative variables. 2. Categorical variables are the same as quantitative variables. 3. Quantitative variables can be continuous variables.
A. 1 only
B. 1 and 3 only
C. 3 only
D. 2 only
76: Which of the following would be appropriate for a z-test?
A. Determining whether the life expectancy of women in a population is statistically different from that of men
B. Determining if a small set of pieces of oak firewood burn longer than pine firewood
C. Determining whether regular exercise decreases the number of new heart disease cases by more than 10% in a year
77: Which one of these variables is a binomial random variable?
A. number of women taller than 68 inches in a random sample of 5 women
B. number of CDs a randomly selected person owns
C. time it takes a randomly selected student to complete a multiple choice exam
D. number of textbooks a randomly selected student bought this term
78: What is the formula for the variance of a population?
A. SQRT( SUM(((x - sample mean)^3) / Number of observations))
B. SUM(((observation - sample mean)^2) / Number of observations)
C. SQRT( SUM)((x - sample mean)^2) / Number of observations))
D. SUM((( - sample mean)^3) / Number of observations)
E. SUM((observation - sample mean) / Number of observations)
79: Suppose you have generated this model to predict income: Income = 10 + .5(Years of Education), units are in thousands, ie 10.5 = $10,500. Interpret Beta1.
A. For every additional year of education, income is expected to increase by $500.
B. For every additional year of education, income is expected to increase by $10,500.
C. At zero years of education, income is expected to be $10,000.
D. At 5 years of education, income is expected to be $25,000.
80: The center line inside a box plot typically represents the _____ in any instance.
A. 2nd Percentile
B. Median of the distribution
C. Inter-quartile Range
D. Average of the distribution
81: A bag contains 4 balls (2 red and 2 blue). You pull out one ball at a time without replacement. What is the probability that the fourth ball chosen is a red ball?
A. 9/16
B. 1/2
C. 5/12
D. 7/12
E. 2/3
82: A manager of a large bank wants to compute the average interest rates across all bonds that the bank invests in. The manager randomly sampled 127 bonds that the bank invests in and calculated the average interest rate over the past year of the sample was 2.47%. What is the parameter of interest in this study?
A. The 127 bonds used in the calculation.
B. 2.47%
C. The average interest rate of all bonds that the bank invests in.
D. All bonds that the bank invests in.
83: Which of the following is a characteristic of an F-distribution?
A. No no lower or upper bound
B. Right Skewed
C. Bimodal
D. Symmetric
84: C(n,r) is equal to...
A. n!/r!
B. n!/(r!(n-r)!)
C. n!r!
D. n!/(n-r)!
85: Symbolism: What does the Greek letter mu represent (without any other symbols) in statistics?
A. Population mean
B. None of the other options
C. Sample standard deviation
D. Population standard deviation
E. Sample mean
86: Which of the following statements are true about confidence intervals for means? 1. The center of the confidence interval is always 0. 2. The bigger the confidence interval, the smaller the margin of error. 3. The bigger your sample, the smaller the margin of error.
A. 2 only
B. 3 only
C. 1 and 2 only
D. 1 only
87: Which of the following is A test of normality?
A. Kolmogrov-Smirnov Test of Normality
B. Test of Data Normality
C. The Standard Test of Normality
D. Time Series Test of Normality
E. Marx's Test of Normality
88: Which of the following examples involves paired data?
A. A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students). The groups were followed for 2 weeks and the proportions with colds were compared.
B. A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.
C. None of the above.
D. A study compared the average number of courses taken by a random sample of 100 freshmen at a university with the average number of courses taken by a separate random sample of 100 freshmen at a community college.
89: When do you fail to reject the null hypothesis?
A. P-Value is > alpha (level of significance)
B. P-Value is < alpha (level of significance)
90: P(n,r) is equal to...
A. n!/(r!(n-r)!)
B. n!r!
C. n!/r!
D. n!/(n-r)!
91: If you have a hypothesis test with a significance level of 0.05 and a p-value of 0.01, what is the result of your hypothesis test?
A. You fail to reject the null hypothesis
B. You reject the null hypothesis
C. You accept the null hypothesis
D. Not enough information.
92: The median grade on a midterm exam in a math class of 60 students is 85. The teacher gives an additional 5 bonus points to the 3 students who scored the highest on the exam. What is the new median grade for the class?
A. Not enough information.
B. 90
C. 80
D. 85
93: P(A)*P(B)=P(A and B) What can you conclude about A and B?
A. They are independent.
B. They are neither independent nor mutually exclusive.
C. They are mutually exclusive.
D. They are independent and mutually exclusive.
94: Say 2 events satisfy the following equation: P(A intersect B) = P(A) x P(B). We say that events A and B are __.
A. Mutually exclusive
B. Disjoint
C. Independent
D. Dependent
95: Where would the outliers be if a distribution had a skewness of -1?
A. No outliers
B. Right
C. Down
D. Left
E. Up
96: What is derived from the third moment of distribution?
A. Kurtosis
B. Variance
C. Skewness
D. Standard Deviation
E. Mean
97: Suppose A is always 3. Var(B)=4. What is Var(A+B)?
A. 7
B. 4
C. 13
D. Not enough information.
E. 0
98: In hypothesis testing, which of the following statements is always true?
A. The P-value is a test statistic.
B. The P-value is computed from the significance level.
C. The P-value is the parameter in the null hypothesis.
D. The P-value is a probability.
99: Suppose E and F are events in a sample space S. Suppose further that E has probability .2, F has probability .6, and the intersection of E and F has probability .1. What is the probability of the union of E and F?
A. .8
B. .7
C. .6
D. .68
100: An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand. Is this an example of a simple random sample?
A. Yes, because each buyer in the sample had an equal chance of being sampled.
B. Yes, because car buyers of every brand were equally represented in the sample.
C. Yes, because each buyer in the sample was randomly sampled.
D. No, because every possible 400-buyer sample did not have an equal chance of being chosen.
List of Statistics & Probabili...
Available in:
Statistics & Probability MCQs
Множественный выбор вопросов по статистике и вероятности (Statistics & Probability MCQs)
Preguntas de opción múltiple de Estadística y Probabilidad (Statistics & Probability MCQs)
統計と確率の多肢選択問題 (Statistics & Probability MCQs)
Domande a risposta multipla di Statistica e Probabilità (Statistics & Probability MCQs)
Questions à choix multiples sur les statistiques et la probabilité (Statistics & Probability MCQs)
Questões de Múltipla Escolha de Estatística e Probabilidade (Statistics & Probability MCQs)
Multiple-Choice-Fragen zu Statistik und Wahrscheinlichkeit (Statistics & Probability MCQs)
统计与概率多项选择题 (Statistics & Probability MCQs)
أسئلة اختيارية متعددة في الإحصاء والاحتمالات (Statistics & Probability MCQs)
Soal Pilihan Ganda Statistik & Probabilitas
İstatistik ve Olasılık Çoktan Seçmeli Soruları
