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GED Math Data, Statistics, and Probability Summary

Checked 10/24/26

Data, Statistics, and Probability: key points

  • The median is the middle value after the data are put in order.
  • Probability = favorable outcomes / total equally likely outcomes.
Importance
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Weight
About 4 of 21 Quantitative Problem Solving questions (20%)

Reading bar graphs, circle graphs, tables, and scatter plots; mean, median, mode, range, and weighted average; counting and simple probability.

📖 See more Data, Statistics, and Probability concepts →

Data, Statistics, and Probability: 10 sample questions

Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 1. A driver made these numbers of deliveries over 5 days: 7, 10, 12, 19, 22. What is the mean (average) number of deliveries per day?

  1. ① 14
  2. ② 12
  3. ③ 15
  4. ④ 70
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Answer: ① 14

Key point: Mean = total of the values ÷ number of values

  1. Add the values: 7 + 10 + 12 + 19 + 22 = 70.
  2. Divide by the number of days: 70 ÷ 5 = 14.

Check: 14 × 5 = 70, which matches the total.

Wrong choices

  • 12: 12 is the median (the middle value), not the mean.
  • 15: 15 is the range (22 − 7), not the mean.
  • 70: 70 is the total; it still has to be divided by 5.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 2. Six workers scored 82, 75, 97, 68, 88, and 79 on a safety test. What is the median score?

  1. ① 79
  2. ② 81.5
  3. ③ 82.5
  4. ④ 80.5
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Answer: ④ 80.5

Key point: Median: order the data; even count = average two middles

  1. Put the scores in order: 68, 75, 79, 82, 88, 97.
  2. There are 6 scores, so there are two middle values: 79 and 82.
  3. Median = (79 + 82) ÷ 2 = 161 ÷ 2 = 80.5.

Check: Three scores (68, 75, 79) are below 80.5 and three (82, 88, 97) are above it.

Wrong choices

  • 81.5: 81.5 is the mean (489 ÷ 6), not the median.
  • 82.5: 82.5 averages the two middle numbers of the unordered list (97 and 68); the data must be put in order first.
  • 79: 79 is only one of the two middle values; with an even count you average both.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 3. A bag holds 5 red, 3 blue, and 4 green marbles. One marble is picked without looking. What is the probability that it is blue?

  1. ① 1/12
  2. ② 3/4
  3. ③ 1/4
  4. ④ 1/3
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Answer: ③ 1/4

Key point: Probability = favorable outcomes ÷ total outcomes

  1. Total marbles: 5 + 3 + 4 = 12.
  2. Blue marbles: 3.
  3. Probability = 3/12 = 1/4.

Check: 1/4 of 12 marbles is 3 marbles, the number of blue ones.

Wrong choices

  • 1/3: 1/3 compares blue to the other marbles (3 out of 9) instead of to all 12.
  • 3/4: 3/4 is the probability of NOT picking blue.
  • 1/12: 1/12 is the chance of picking one particular marble, but there are 3 blue ones.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 4. A shoe store sold these sizes in one hour: 9, 10, 9, 11, 8, 10, 9, 12. What is the mode?

  1. ① 9.75
  2. ② 10
  3. ③ 9
  4. ④ 4
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Answer: ③ 9

Key point: Mode = the value that appears most often

  1. Count each size: 8 appears once, 9 appears 3 times, 10 appears 2 times, 11 once, 12 once.
  2. The size that appears most often is 9.

Check: No other size appears 3 or more times.

Wrong choices

  • 10: 10 appears only twice; 9 appears three times.
  • 9.75: 9.75 is the mean (78 ÷ 8), not the mode.
  • 4: 4 is the range (12 − 8), not the mode.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 5. The high temperatures for five days were 54°F, 61°F, 48°F, 70°F, and 66°F. What is the range of these temperatures?

  1. ① 22 degrees
  2. ② 16 degrees
  3. ③ 59.8 degrees
  4. ④ 70 degrees
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Answer: ① 22 degrees

Key point: Range = largest value − smallest value

  1. Largest value: 70. Smallest value: 48.
  2. Range = 70 − 48 = 22 degrees.

Check: Every temperature lies between 48 and 70, a spread of 22 degrees.

Wrong choices

  • 16 degrees: 16 degrees subtracts the first temperature listed (54) from the highest (70); the range uses the smallest value, 48.
  • 70 degrees: 70 is the highest value, not the range.
  • 59.8 degrees: 59.8 is the mean (299 ÷ 5), not the range.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 6. A food truck recorded its sales for four days: Monday $40, Tuesday $55, Wednesday $35, Thursday $70. What percent of the four-day total came from Thursday?

  1. ① 50%
  2. ② 25%
  3. ③ 70%
  4. ④ 35%
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Answer: ④ 35%

Key point: Percent of total = part ÷ whole × 100

  1. Total sales: 40 + 55 + 35 + 70 = $200.
  2. Thursday's share: 70 ÷ 200 = 0.35.
  3. 0.35 × 100 = 35%.

Check: 35% of $200 is $70.

Wrong choices

  • 70%: 70% uses Thursday's dollar amount as the percent without dividing by the total.
  • 25%: 25% assumes each of the 4 days had an equal share.
  • 50%: 50% is too high; half of $200 would be $100, not $70.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 7. To earn a certificate, a trainee needs an average of exactly 85 on five quizzes. Her first four scores are 80, 90, 78, and 88. What score does she need on the fifth quiz?

  1. ① 84
  2. ② 89
  3. ③ 85
  4. ④ 91
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Answer: ② 89

Key point: Missing value = (mean × count) − sum of the others

  1. Total needed: 85 × 5 = 425.
  2. Sum so far: 80 + 90 + 78 + 88 = 336.
  3. Fifth score: 425 − 336 = 89.

Check: (80 + 90 + 78 + 88 + 89) ÷ 5 = 425 ÷ 5 = 85.

Wrong choices

  • 85: 85 would give a total of 421 and an average of 84.2.
  • 84: 84 is the average of the first four scores, not the score she needs.
  • 91: 91 would give a total of 427 and an average of 85.4.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 8. In a training course, tests count for 60% of the grade and homework counts for 40%. Jamal has a test average of 75 and a homework average of 90. What is his course grade?

  1. ① 81
  2. ② 165
  3. ③ 82.5
  4. ④ 84
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Answer: ① 81

Key point: Weighted average: multiply each score by its weight, add

  1. Tests: 0.60 × 75 = 45.
  2. Homework: 0.40 × 90 = 36.
  3. Course grade: 45 + 36 = 81.

Check: The grade should be closer to 75 than to 90, because tests count more. 81 is.

Wrong choices

  • 82.5: 82.5 is the plain average of 75 and 90; it ignores the weights.
  • 84: 84 switches the weights (40% for tests and 60% for homework).
  • 165: 165 adds the two averages without using the weights.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 9. A survey asked 20 households how many children live there. Results: 3 households have 0 children, 5 have 1 child, 8 have 2 children, and 4 have 3 children. What is the mean number of children per household?

  1. ① 1.65
  2. ② 8.25
  3. ③ 1.5
  4. ④ 2
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Answer: ① 1.65

Key point: Mean from counts: Σ(value × count) ÷ total count

  1. Total children: 0 × 3 + 1 × 5 + 2 × 8 + 3 × 4 = 0 + 5 + 16 + 12 = 33.
  2. Total households: 3 + 5 + 8 + 4 = 20.
  3. Mean: 33 ÷ 20 = 1.65.

Check: 1.65 × 20 = 33 children.

Wrong choices

  • 1.5: 1.5 averages the values 0, 1, 2, 3 without counting how many households have each.
  • 8.25: 8.25 divides the 33 children by the 4 groups instead of by the 20 households.
  • 2: 2 is the mode (the most common answer), not the mean.
Practice questionReviewedQuantitative Problem Solving › Data, Statistics, and Probability★★★★☆

Question 10. A sandwich shop offers 4 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. A sandwich has one of each. How many different sandwiches are possible?

  1. ① 60
  2. ② 15
  3. ③ 12
  4. ④ 20
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Answer: ① 60

Key point: Counting: multiply the number of choices at each step

  1. For each step, multiply the number of choices.
  2. 4 × 5 × 3 = 60 sandwiches.

Check: With one bread there are 5 × 3 = 15 meat-and-cheese pairs. Four breads give 4 × 15 = 60.

Wrong choices

  • 12: 12 adds the choices (4 + 5 + 3) instead of multiplying.
  • 20: 20 counts only bread and meat (4 × 5) and leaves out the cheese.
  • 15: 15 counts only meat and cheese (5 × 3) and leaves out the bread.

Test yourself.

Data, Statistics, and Probability: 5 questions →Quantitative Problem Solving: 5 questions →

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