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Praxis Mathematics: Statistics and Probability

Data, chance, and sampling for secondary mathematics, including decisions about student work and misleading summaries.

Teacher certification exams are administered by testing organizations. FreeExam is not affiliated with those organizations, and these questions are original practice, not an official test.

Praxis is a trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.The scores are 4, 4, and 10. What is the mean?

  2. 2.The values are 1, 4, 9, 9, and 20. What is the median?

  3. 3.The values are 2, 5, 5, 5, 8, and 8. What is the mode?

  4. 4.The values are 3, 3, 7, and 11. What is the range?

  5. 5.A data set is 2, 3, 4, 5, and 100. Which measure is pulled the most by the value 100?

  6. 6.For the ordered list 2, 4, 6, 8, 10, 12, the lower half is 2, 4, 6 and the upper half is 8, 10, 12. What is the interquartile range?

  7. 7.A fair coin is tossed once. What is the probability of heads?

  8. 8.A bag has 3 red marbles and 1 blue marble. One marble is drawn at random. What is the probability it is blue?

  9. 9.Two fair coins are tossed. The tosses are independent. What is the probability both land heads?

  10. 10.The probability of rain tomorrow is 0.3. What is the probability it does not rain?

  11. 11.Events A and B cannot happen together. P(A) = 0.2 and P(B) = 0.5. What is P(A or B)?

  12. 12.A fair six-sided die is rolled once. What is the probability the result is even?

  13. 13.A student draws a card, keeps it, and draws a second card from what is left. Which description fits?

  14. 14.A game pays $10 with probability 0.2 and pays $0 otherwise. What is the expected payout?

  15. 15.A scatterplot shows that larger x-values tend to come with larger y-values. Which association is that?

  16. 16.Towns with more ice-cream sales also have more swimming accidents. A student says ice cream causes the accidents. What is the better reading?

  17. 17.A model predicts y = 5 for a point whose observed y-value is 8. What is the residual?

  18. 18.A fitted line says the predicted score rises by 2 points for each extra hour of practice. What is the slope?

  19. 19.A large set is approximately normal. About what percent of the values lie within one standard deviation of the mean?

  20. 20.A score is 85. The mean is 70 and the standard deviation is 5. What is the z-score?

  21. 21.A school asks only the chess club whether students like chess, then reports the result as the preference of the whole school. What is the problem?

  22. 22.Which method gives every student in a school the same chance to be chosen?

  23. 23.Two classes have the same mean test score. Class A has a larger standard deviation. What does that say?

  24. 24.On a box plot, what does the box itself span?

  25. 25.A student uses a bar graph with gaps for the heights of 30 plants measured in centimeters. Which display fits the measurement better?

  26. 26.A bar graph of scores starts the vertical axis at 50. The bars for 52 and 54 look very different in height. What should a reader notice?

  27. 27.How many ways can 2 students be chosen from a group of 4, when order does not matter?

  28. 28.How many orders are there for 3 distinct books on a shelf?

  29. 29.Two fair coins are tossed. What is the probability of at least one head?

  30. 30.Of 4 students in the band, 3 are also in the choir. A student is chosen at random from the band. What is the probability that student is in the choir?

  31. 31.A two-way table shows 20 students: 8 play soccer, and 5 of those 8 also run track. Of the 12 who do not play soccer, 3 run track. How many students run track?

  32. 32.Every value in a data set equals 7. What is the standard deviation?

  33. 33.A teacher adds 5 points to every score. What happens to the mean and the standard deviation?

  34. 34.Every value in a data set is multiplied by 2. What happens to the standard deviation?

  35. 35.The ordered list is 3, 5, 8, and 10. What is the median?

  36. 36.A quiz is 20% of the grade and a test is 80%. A student scores 100 on the quiz and 50 on the test, then averages 100 and 50 to get 75. What is the weighted grade?

  37. 37.A student lists probabilities 0.2, 0.3, and 0.6 for three outcomes that cover every result and do not overlap. What is wrong?

  38. 38.Events A and B are independent, and both have probability 0.4. Can they be mutually exclusive?

  39. 39.A normal curve has mean 20. Which statement is true?

  40. 40.A distribution has a long tail to the left. Which comparison is the usual one?

  41. 41.A teacher records the heights of every student in one class and computes their mean. For a claim about that class only, what is the set of heights?

  42. 42.A random sample grows from 25 to 400, and the method stays the same. What usually happens to the margin of error?

  43. 43.A fair coin is tossed many times. What does the law of large numbers say about the proportion of heads?

  44. 44.In 10 tosses, a fair coin lands heads 8 times. A student says the coin must be unfair. What is a sound reply?

  45. 45.A line fit to study times from 0 to 4 hours is used to predict a score at 40 hours. What is the risk?

  46. 46.One point sits far from a tight linear cloud and far from the mean of x. Removing it changes the fitted slope a lot. What is that point?

  47. 47.A correlation coefficient is about 0. Which description fits?

  48. 48.A correlation is −0.95. Which description fits?

  49. 49.A student reports a probability of 1.2. What feedback fits?

  50. 50.The odds in favor of an event are 1 to 3. What is the probability of the event?

  51. 51.A student has 3 shirts and 2 pairs of pants. An outfit is one shirt and one pair of pants. How many outfits are there?

  52. 52.A deck has 2 aces and 3 other cards, 5 cards in all. Two cards are drawn without replacement. What is the probability both are aces?

  53. 53.A spinner has two equal sections, labeled win and lose. It is spun twice. What is the probability of exactly one win?

  54. 54.A data set has standard deviation 3. What is its variance?

  55. 55.The five-number summary of a set is 2, 5, 7, 9, 14. What is the median?

  56. 56.A class mean is 80. One student scores 80. What is that student's deviation from the mean?

  57. 57.A student says the median of 1, 2, 3, 4, and 100 is 100, because the median should notice the outlier. What is the median?

  58. 58.Which event has probability 0 in a single roll of a fair six-sided die?

  59. 59.Which event has probability 1 in a single roll of a fair six-sided die?

  60. 60.P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2. What is P(A or B)?

  61. 61.Are the events in the previous kind of table independent when P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2?

  62. 62.A residual plot shows a clear curve, not a random scatter. What does that suggest about a straight-line model?

  63. 63.The mean of four scores is 10. What is the sum of the scores?

  64. 64.A sample is chosen by picking every 10th name on a randomly started roster. What kind of sample is that?

  65. 65.A poll is posted online and only readers who click it are counted. What is the main risk?

  66. 66.A data set is 1, 2, 3. A student computes the mean as 1 + 2 + 3 = 6. What is missing?

  67. 67.Two events partition a sample space. P(A) = 0.15. What is P(not A)?

  68. 68.A line of best fit has slope −4. Which reading is right?

  69. 69.The values 4, 4, 4, and 4 have which mean, median, and mode?

  70. 70.A teacher asks why a random sample is used instead of asking only friends. Which reason is sound?

  71. 71.A probability model assigns 1/2, 1/3, and 1/6 to three outcomes. Is the model possible?

  72. 72.An observational study finds that students who sit in front have higher scores. What can it support?

  73. 73.A bag has 5 red and 5 blue marbles. One is drawn and replaced, then another is drawn. What is the probability both are red?

  74. 74.The ordered data are 6, 7, 8, 9, 20. A student reports the mean and the median as the same number. Which pair is right?

  75. 75.A simulation of a spinner is run 20 times and produces 9 wins. The model says the probability of a win is 1/2. What is a fair conclusion?

  76. 76.Which graph is a better comparison of two categories when one category has 12 items and the other has 4?

  77. 77.The correlation between shoe size and score on a memory quiz, for a random sample of adults, is about 0.05. Which conclusion fits?

  78. 78.A census of a club of 18 members finds that 12 prefer mornings. For that club, what is the proportion who prefer mornings?

  79. 79.Scores are 10, 10, 10, and 50. Which measure should a teacher quote if the goal is a typical score that is not dragged by 50?

  80. 80.A student builds a tree for two coin tosses and lists only H and T, two branches total. What is missing?

  81. 81.P(A) = 0.3 and P(B|A) = 0.5. What is P(A and B)?

  82. 82.A set has mean 12 and a new value equal to 12 is added. What happens to the mean?

  83. 83.Which design can support a cause-and-effect claim better than an observational study, when it is done carefully?

  84. 84.A histogram has a bar from 0 to 10 with count 4, and a bar from 10 to 20 with count 6. How many values are in the data set?

  85. 85.A student says a correlation of 1.2 means a very strong line. What is the correction?

  86. 86.The interquartile range of a set is 4, and every value is increased by 3. What is the new interquartile range?

  87. 87.A game costs $1 to play. It pays $5 with probability 0.1 and pays $0 otherwise. What is the expected net gain, including the cost?

  88. 88.Which pair of variables is most likely to show a negative association?

  89. 89.A population has 200 juniors and 50 seniors. A sample takes 10% of each class. How many students are in the sample, and what is the design?

  90. 90.A student double-counts the overlap and gets P(A or B) = 0.9 when P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2. What should the teacher have the student subtract?

  91. 91.The standard deviation of a sample is reported as −2. What is the error?

  92. 92.A fitted line is ŷ = 3 + 2x. What is the predicted y when x = 4?

  93. 93.For that same line, a point has x = 4 and observed y = 9. What is the residual?

  94. 94.Which sampling method names groups, such as classrooms, and then includes every person in each chosen group?

  95. 95.A normal distribution has mean 100 and standard deviation 10. About what percent of values are above 100?

  96. 96.Using that same normal model, a value of 120 is how many standard deviations above the mean?

  97. 97.A student computes a five-number summary and draws the box from the minimum to the maximum. What should the box use?

  98. 98.Two fair dice are rolled. What is the probability the faces sum to 2?

  99. 99.Two fair dice are rolled. What is the probability the faces sum to 7?

  100. 100.A researcher measures the same 15 runners before and after a training plan. The comparison uses paired differences. Why pair them?

  101. 101.A data set has quartile values 10 and 18. A value is marked as an outlier by the 1.5-IQR rule only if it is far enough from the quartiles. What is the IQR, and how far is 1.5 IQR?

  102. 102.Which question is a statistical question rather than a question with one fixed answer?

  103. 103.A student says the experimental probability of heads is 7/10 after 7 heads in 10 tosses, so the theoretical probability has become 7/10. What is the distinction?

  104. 104.The mean of 5, 5, and 8 is 6. A student says the mean must be one of the data values. What is the reply?

  105. 105.A survey asks, 'Do you agree that the unfair new rule should be canceled?' What is the flaw?

  106. 106.Which display shows every individual value rather than grouping the values into bins?

  107. 107.A chance process is repeated, and the result of one trial does not change the probabilities of the next trial. What is that property called?

  108. 108.A class summary reports only the mean. Two sections both have mean 75, but one has scores from 70 to 80 and the other has scores from 40 to 100. What else should the report include?