GED Math: Data, Statistics, and Probability Concepts
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Overview
This chapter covers reading data from tables, bar graphs, circle graphs, dot plots, box plots, and scatter plots, and describing data with the mean, median, mode, and range. It also covers weighted averages, counting the number of possible outcomes, and finding probabilities.
The mean is the total divided by the number of values. The median is the middle value after the data are put in order; with an even number of values it is the mean of the two middle values. The mode is the value that appears most often, and the range is the largest value minus the smallest. A box plot shows the middle half of the data inside the box, and the length of the box is the interquartile range.
A weighted average multiplies each value by its weight before adding. When a needed average is given, multiply it by the number of values to get the total needed, then subtract the values you already have to find the missing one.
To count choices made in steps, multiply the number of options at each step. When order matters, as with different jobs, the count is a permutation; when order does not matter, as with a committee, divide out the repeated orders to get a combination. Probability is the number of favorable outcomes divided by the total number of equally likely outcomes.
Key concepts
Mean and median
Mean = total of the values ÷ number of values. Median = middle value of the ordered data, or the mean of the two middle values when the count is even.
Memory tipAlways put the data in order before finding the median.
Source: GED Testing Service (Mathematics Formula Sheet) · as of 2026
Mode and range
The mode is the most frequent value. The range is the largest value minus the smallest value.
Memory tipRange uses the smallest and largest values, not the first and last in the list.
Weighted average
Multiply each value by its weight (or count), add the results, and divide by the total weight.
Memory tipIf weights are percents that add to 100%, just multiply and add.
Counting principle
If one choice has m options and another has n options, there are m × n ways to make both choices.
Memory tipMultiply, do not add, the options at each step.
Permutations and combinations
Permutation: order matters (6 × 5 × 4 ways to fill 3 different jobs from 6 people). Combination: order does not matter, so divide by the number of ways to arrange the chosen group.
Memory tipDifferent roles: permutation. Same role (a team): combination.
Probability
Probability = favorable outcomes ÷ total equally likely outcomes. For two independent events both happening, multiply their probabilities. Without replacement, the second pick has one fewer item.
Memory tipProbability is always between 0 and 1.
Often tested
- Missing value = (needed average × number of values) − sum of the known values.
- In a box plot, the line inside the box is the median, and the box length is the interquartile range.
- Mean from a frequency table: multiply each value by its count, then divide by the total count.
- "And" for independent events means multiply; "not" means 1 minus the probability.
Easy to confuse: Permutation and combination
| Item | Permutation | Combination |
|---|---|---|
| Order matters? | Yes | No |
| Example | Driver, loader, checker from 6 workers | A 3-person committee from 7 workers |
| Count | 6 × 5 × 4 = 120 | (7 × 6 × 5) ÷ (3 × 2 × 1) = 35 |
3 sample questions
Verified practice questions from this unit.
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 14
- ② 12
- ③ 15
- ④ 70
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Answer: ① 14
Key point: Mean = total of the values ÷ number of values
- Add the values: 7 + 10 + 12 + 19 + 22 = 70.
- 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.
Question 2. Six workers scored 82, 75, 97, 68, 88, and 79 on a safety test. What is the median score?
- ① 79
- ② 81.5
- ③ 82.5
- ④ 80.5
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Answer: ④ 80.5
Key point: Median: order the data; even count = average two middles
- Put the scores in order: 68, 75, 79, 82, 88, 97.
- There are 6 scores, so there are two middle values: 79 and 82.
- 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.
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 1/12
- ② 3/4
- ③ 1/4
- ④ 1/3
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Answer: ③ 1/4
Key point: Probability = favorable outcomes ÷ total outcomes
- Total marbles: 5 + 3 + 4 = 12.
- Blue marbles: 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.
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