8.3 Probability, Statistics, and Data Displays
Key Takeaways
- GED Math data questions require reading the display before calculating, including titles, labels, scales, units, and keys.
- Mean, median, mode, and range describe data in different ways, so the best measure depends on the question and the data set.
- A missing value from an average can be found by multiplying the mean by the number of data values, then subtracting the known values.
- Simple probability is favorable outcomes divided by total equally likely outcomes, and compound probability depends on whether events are independent or connected.
- Bar graphs, circle graphs, dot plots, histograms, box plots, scatter plots, and tables can all appear as GED-style data displays.
Read the Display Before the Numbers
GED Math data questions are designed to test interpretation, not just arithmetic. The official assessment targets include bar graphs, circle graphs, dot plots, histograms, box plots, tables, scatter plots, mean, median, mode, range, weighted average, and probability. That sounds like many topics, but the routine is consistent: read the title, read the labels, check the scale, then answer only what the display supports.
A graph scale can change everything. If a bar graph increases by 5 on each grid line, a bar halfway between 20 and 25 is not 21. If a circle graph gives percentages, the parts must be converted to counts only when the question gives a total. If a scatter plot shows an upward pattern, it suggests association, but GED Math focuses on interpreting the graph rather than claiming one variable causes the other.
Statistics Quick Table
| Measure | How to find it | GED use |
|---|---|---|
| Mean | Add values and divide by count | Average amount or equal sharing |
| Median | Order values and find the middle | Typical value when outliers exist |
| Mode | Most frequent value | Most common response or category |
| Range | Largest minus smallest | Spread from low to high |
| Weighted average | Total weighted points divided by total weights | Different counts or categories with different values |
Worked Mean and Missing-Value Example
Suppose four quiz scores are 72, 80, 85, and 91. The mean is (72 + 80 + 85 + 91) / 4 = 328 / 4 = 82. If the question asks for the median, first order the data. It is already ordered, and with four values the median is the average of the two middle values: (80 + 85) / 2 = 82.5.
For a missing value, work backward from the total. Suppose five delivery times have a mean of 24 minutes. Four times are 18, 22, 25, and 30 minutes. The total for five times must be 5 * 24 = 120 minutes. The known total is 18 + 22 + 25 + 30 = 95 minutes. The missing time is 120 - 95 = 25 minutes.
Data Displays
A dot plot shows individual data values on a number line, so it is useful for counting frequency. A histogram groups numerical values into intervals, so it is useful for seeing distribution. A box plot shows minimum, quartiles, median, and maximum. A scatter plot compares two variables, such as hours studied and practice score. A bar graph compares categories, while a circle graph shows parts of a whole.
Probability Routine
Simple probability is favorable outcomes / total equally likely outcomes. If a bag has 5 red tiles, 3 blue tiles, and 2 green tiles, the probability of drawing blue is 3 / 10. The probability of not drawing blue is 7 / 10 because 7 tiles are not blue.
For compound events, decide whether the first event changes the second. If a coin is flipped and a number cube is rolled, the events are independent, so multiply probabilities: P(heads and 4) = 1/2 * 1/6 = 1/12. If two tiles are drawn without replacement, the first draw changes the total for the second draw.
GED Data Checklist
- Identify the data source: table, graph, plot, or word problem.
- Check whether the question asks for a count, percent, statistic, or probability.
- Order data before finding a median.
- Use total = mean * count for missing-average problems.
- Reduce probability fractions only after the setup is correct.
The most common wrong answers come from skipping step 1. If you read a bar label as the value, ignore the axis scale, forget to order the data, or treat a without-replacement draw as independent, the arithmetic may look neat but still answer the wrong question.
The data set shows weekly study hours: 2, 3, 3, 4, 8. Which statement is true?
A jar contains 6 black pens, 4 blue pens, and 5 red pens. If one pen is chosen at random, what is the probability that it is blue?