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Praxis Middle School Mathematics: Statistics and Probability

Means, medians, probability, and samples for middle school, including what to do when a student's statistics goes wrong.

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 quiz scores are 6, 8, and 10. What is the mean?

  2. 2.The ordered times in minutes are 3, 7, 9, 12, and 15. What is the median?

  3. 3.The shoe sizes are 6, 7, 7, 7, and 9. What is the mode?

  4. 4.The temperatures are 11, 14, 14, and 20. What is the range?

  5. 5.The ages are 4, 5, 5, and 30. Which measure is pulled the most by the age 30?

  6. 6.A spinner has 4 equal sections: red, blue, green, and yellow. What is the probability of red?

  7. 7.A bag has 2 red tiles and 6 blue tiles. One tile is drawn at random. What is the probability it is red?

  8. 8.The probability that a bus is late is 0.15. What is the probability it is not late?

  9. 9.A fair six-sided die is rolled once. What is the probability the result is greater than 4?

  10. 10.Two events cannot happen together. Their probabilities are 0.1 and 0.4. What is the probability that one or the other happens?

  11. 11.A student finds the mean of 2, 2, 2, and 10 by dividing the sum by 2, the mode. What is the mean?

  12. 12.The ordered list is 1, 4, 8, and 10. What is the median?

  13. 13.A class records 12 students who walk and 8 who ride. What is the relative frequency of walking?

  14. 14.Which question is best answered by a random sample of the school's eighth graders?

  15. 15.A number cube is fair. The probability of rolling a 3 is 1/6. What is the probability of rolling a number that is not 3?

  16. 16.The values 5, 5, and 5 have which mean, median, and mode?

  17. 17.A game board has 10 equally likely spaces, and 3 of them give a prize. What is the probability of a prize?

  18. 18.A dot plot of hours of practice shows values at 1, 1, 2, 2, 2, and 8. A student says the typical student practices 8 hours. Which measure did the student report?

  19. 19.Each letter of the word MATH is written on a card. One card is drawn at random. What is the probability the letter is a vowel?

  20. 20.Adding 10 to every value in a data set does what to the mean?

  21. 21.A bar graph starts the vertical scale at 40 instead of 0. The bars for 42 and 46 look very different in height. What is the risk?

  22. 22.Two fair coins are tossed. The tosses do not affect each other. What is the probability of tails and then tails?

  23. 23.The ordered data are 2, 6, 6, 6, and 20. What is the median?

  24. 24.A student says a probability of 1.2 is possible for drawing a red marble. What should the teacher say?

  25. 25.In a survey, 18 of 24 students chose band. What percent chose band?

  26. 26.A teacher asks only the students in chess club whether the school should fund chess. What is the problem with using that result for the whole school?

  27. 27.The data are 9, 9, 12, and 14. What is the mean?

  28. 28.A spinner has 5 equal sections labeled 1 through 5. What is the probability of an even number?

  29. 29.Which display is most useful for showing how one quantity changes over seven months?

  30. 30.The probability of picking a green card is 1/5. There are 20 cards. How many are green?

  31. 31.A data set has mean 20. Every value is multiplied by 3. What is the new mean?

  32. 32.A student lists the outcomes of two coin tosses as H and T only, leaving out mixed results. How many equally likely outcomes are there?

  33. 33.The heights in inches are 60, 62, 62, and 64. What is the range?

  34. 34.Which probability is impossible?

  35. 35.Five students have scores 70, 70, 80, 90, and 90. What is the median?

  36. 36.A sample of 30 students is chosen by drawing names so that each student in the school has the same chance. What kind of sample is that?

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

  38. 38.The counts of pets are 0, 1, 1, 2, and 6. What is the mode?

  39. 39.A student computes the range of 4, 9, and 13 as 4 + 13 = 17. What is the range?

  40. 40.Which event has probability 0?

  41. 41.The test scores are 40, 50, 50, 50, and 60. What is the mean?

  42. 42.A circle graph shows 1/4 of the students chose art. There are 32 students. How many chose art?

  43. 43.Why might the median describe typical rent better than the mean when one rent is far above the others?

  44. 44.A jar has 4 green and 1 yellow counter. One counter is drawn. What is the probability it is yellow?

  45. 45.The ordered values are 3, 5, 8, 10, 14, and 16. What is the median?

  46. 46.A student predicts a coin will land heads because the last three tosses were tails. What should the teacher point out?

  47. 47.The numbers of books read are 1, 2, 2, 3, and 12. What is the median?

  48. 48.Which comparison of two classes is fair when the classes have different sizes?

  49. 49.A fair die is rolled once. What is the probability of a 1 or a 2?

  50. 50.The data 8, 8, 8, and 8 have range equal to what?

  51. 51.A line plot shows four dots at 3 and one dot at 7. What is the mean?

  52. 52.Which sample is most likely to represent a town's adults?

  53. 53.P(win) = 0.6 for a game that is played once. What is P(not win)?

  54. 54.The prices are $3, $3, $5, and $9. What is the mode?

  55. 55.A probability experiment is repeated 50 times and an outcome occurs 10 times. What is the experimental probability?

  56. 56.A histogram uses bins 0–9, 10–19, and 20–29. A value of 19 belongs in which bin?

  57. 57.The scores 10, 20, and 30 have mean 20. A fourth score of 20 is added. What is the new mean?

  58. 58.Which statement about a random sample of 20 and a random sample of 200 from the same population is the usual expectation?

  59. 59.A bag has 3 white and 9 black marbles. What is the probability of drawing white?

  60. 60.A student says the mean of 1, 2, and 9 is the middle number, 2. What is the mean?

  61. 61.Two different students are picked at random from a group of 5, without repeating a student. Are the picks independent?

  62. 62.The minutes of homework are 20, 25, 30, 35, and 40. What is the range?

  63. 63.A spinner is 1/2 red and 1/2 blue. It is spun twice. What is the probability of red then blue?

  64. 64.A class mean is 82. One score was entered as 50 instead of 80. What happens to the mean when the score is corrected?

  65. 65.Which of these is a statistical question?

  66. 66.The values are 6, 10, and 14. A student says the median is 10 and the mean is also 10. Is the student right?

  67. 67.A survey asks, "You do want a longer lunch, don't you?" What is the main problem?

  68. 68.There are 8 equally likely names in a drawing, and 2 of the names are Kim. What is the probability the drawn name is Kim?

  69. 69.The daily highs are 70, 72, 74, and 76. What is the mean?

  70. 70.A teacher wants students to see that an outlier moves the mean more than the median. Which set makes that comparison easy?

  71. 71.A coin is fair. In 80 tosses, about how many heads are expected?

  72. 72.The categories of a bar graph are dog, cat, and bird. The bar heights are 6, 3, and 3. How many students answered?

  73. 73.A bag has 7 marbles, all blue. What is the probability of drawing a blue marble?

  74. 74.The ordered ages are 11, 12, 13, 14, and 40. What is the median?

  75. 75.Which graph is a better choice for showing parts of a single whole, such as the share of a budget?

  76. 76.Two independent outcomes each have probability 1/3. What is the probability both happen?

  77. 77.The data are 2, 5, 5, 5, and 8. What is the mode?

  78. 78.A student divides the sum 30 by the range 5 and calls 6 the mean. There are 3 values. What is the mean?

  79. 79.In a random sample of 40 students, 10 play soccer. About what fraction of the school should a student estimate play soccer, if the sample is a good one?

  80. 80.The probabilities of three outcomes that cover every possibility and do not overlap are 0.2, 0.5, and an unknown value. What is the unknown probability?

  81. 81.Which set has mean 6?

  82. 82.A spinner lands on red 30 times in 100 spins. What is the experimental probability of red?

  83. 83.The ordered data are 4, 4, 7, 9, and 9. What is the median?

  84. 84.Why is "Do you agree that the best students join the club?" a weak survey question?

  85. 85.A number from 1 through 10 is picked at random. What is the probability it is 10?

  86. 86.The values 15, 18, and 21 have what range?

  87. 87.A student claims the probability of rain is 1/2 because there are two choices, rain or no rain. The forecast says 1/10. What is wrong with the student's reasoning?

  88. 88.Which measure is best for the most common shoe size in a class?

  89. 89.Four students scored 80, 85, 90, and 95. What is the mean?

  90. 90.A marble is drawn and not replaced. The bag started with 4 red and 1 blue. The first marble was red. What is the probability the second is blue?

  91. 91.The data 5, 8, 8, and 11 have median equal to what?

  92. 92.A class collects the number of siblings for each student. Which question matches that data?

  93. 93.A chance experiment has 5 equally likely outcomes. Three of them are favorable. What is the probability?

  94. 94.The mean of four numbers is 9. What is their sum?

  95. 95.A student says two events are independent because they were listed in the same problem. Which pair is independent?

  96. 96.The temperatures 48, 51, 53, and 60 have range equal to what?

  97. 97.A pie chart shows 25% of the votes for one choice. There were 80 votes. How many votes was that?

  98. 98.Which conclusion is supported by a random sample of 100 students in one school?

  99. 99.The scores are 2, 4, 6, and 8. What is the mean?

  100. 100.A student finds the median of 1, 9, 3 by using the list in that order and choosing 9. What is the median?

  101. 101.A game awards a prize on 1 of 5 equally likely spins. In 40 spins, about how many prizes are expected?

  102. 102.Which pair of measures can be equal even when the data are not all the same number?

  103. 103.A census of a class asks every student in that class. What is true of the result?

  104. 104.The probability of an event is 0.05. Which description fits?

  105. 105.The values 7, 7, 10, and 16 have what mean?

  106. 106.A double bar graph compares two years. The vertical scale is marked in tens. What does the height of a bar show?

  107. 107.Without looking, a student picks one letter from A, B, C, D, and E. What is the probability the letter comes before C in the alphabet?

  108. 108.A student averages 70, 80, and 90 and gets 60 by dividing the sum by 4. What should the teacher have the student count?