8.3 Probability, Statistics, and Data Displays
Key Takeaways
- GED Math data questions require reading the display first: title, axis labels, scale, units, and any key or legend before calculating.
- Mean, median, mode, and range describe data differently, so the right measure depends on the question and on whether outliers are present.
- A missing value behind an average is found by computing total = mean * count, then subtracting the known values.
- Simple probability is favorable outcomes divided by total equally likely outcomes; compound probability depends on whether the events are independent or change one another.
- Bar graphs, circle graphs, dot plots, histograms, box plots, scatter plots, and two-way tables can all appear as GED data displays.
Read the Display Before the Numbers
GED Math data items test interpretation, not just arithmetic. The official assessment targets include bar graphs, circle graphs, dot plots, histograms, box plots, two-way tables, scatter plots, mean, median, mode, range, weighted average, and probability. That is a long list, but the routine is identical every time: read the title, read the labels, check the scale, then answer only what the display supports.
The scale changes everything. If a bar graph rises by 5 per gridline, a bar halfway between 20 and 25 is 22.5, not 21. If a circle graph gives percentages, convert to counts only when a total is provided; 30% of an unstated whole is not a number. If a scatter plot trends upward, it suggests association, but GED Math asks you to describe the pattern (positive, negative, or none; linear or nonlinear; presence of an outlier), not to claim that one variable causes the other.
Statistics Quick Table
| Measure | How to find it | GED use |
|---|---|---|
| Mean | Add all values, divide by the count | Average amount, equal sharing |
| Median | Order the values, take the middle | Typical value when outliers exist |
| Mode | The most frequent value | Most common response or category |
| Range | Largest value minus smallest | Spread from low to high |
| Weighted average | Sum of (value x weight), divided by total weight | Categories with different counts |
The mean is pulled toward extreme values, so when a data set has one very large or very small number, the median is the better 'typical' measure. Test items often hinge on exactly that distinction.
Worked Mean, Median, and Missing-Value Examples
Suppose four quiz scores are 72, 80, 85, and 91. The mean is (72 + 80 + 85 + 91) / 4 = 328 / 4 = 82. For the median of an even-sized list, average the two middle values once the data are ordered: (80 + 85) / 2 = 82.5. Always order before finding a median; an unordered list is the single most common median error.
Missing-value (work-backward) example. Five delivery times have a mean of 24 minutes. Four of them are 18, 22, 25, and 30. The total must be 5 * 24 = 120 minutes. The known total is 18 + 22 + 25 + 30 = 95. The missing time is 120 - 95 = 25 minutes. The formula total = mean * count is the engine of nearly every GED average problem, including 'what score do I need on the last test?' items.
Weighted-average example. A grade is 40% homework and 60% exam. With homework 90 and exam 80, the grade is 0.40 * 90 + 0.60 * 80 = 36 + 48 = 84, not the simple average of 85. The weights, not the raw count of categories, decide the result.
Data Displays at a Glance
- Dot plot: each dot is one value on a number line; good for counting frequency and spotting the mode.
- Histogram: groups numerical data into equal intervals (bins); shows distribution shape.
- Box plot: marks minimum, lower quartile, median, upper quartile, and maximum; the box spans the interquartile range.
- Scatter plot: compares two variables, such as hours studied versus score.
- Bar graph: compares separate categories; circle graph: shows parts of one whole.
Probability Routine
Simple probability is favorable outcomes divided by total equally likely outcomes. If a bag holds 5 red, 3 blue, and 2 green tiles (10 total), then P(blue) = 3/10 and P(not blue) = 7/10, because the complement of an event is 1 minus its probability.
For compound events, decide whether the first event changes the second. A coin flip and a number-cube roll are independent, so multiply: P(heads and a 4) = 1/2 * 1/6 = 1/12. Drawing two tiles without replacement is dependent: after pulling one blue from the 10-tile bag, only 2 blue remain among 9 tiles, so P(blue, then blue) = 3/10 * 2/9 = 6/90 = 1/15. Treating a without-replacement draw as independent is a built-in trap answer. The word or usually means add (after avoiding double-counting), while and for independent events means multiply.
GED Data Checklist
- Identify the source: table, graph, plot, or word problem.
- Decide whether the item wants a count, a percent, a statistic, or a probability.
- Order the data before finding a median.
- Use total = mean * count for any missing-average problem.
- Reduce probability fractions only after the setup is correct.
The most common wrong answers come from skipping step 1. Misreading a bar height, ignoring the axis scale, forgetting to order data, or treating a without-replacement draw as independent all produce arithmetic that looks tidy yet answers the wrong question.
Percent and probability overlap. GED probability is often phrased as a percent or a fraction, and a probability can never exceed 1 (or 100%). If you compute 4/3 or 120%, the setup is wrong, usually because favorable and total were reversed. To convert, 3/10 is 0.30 is 30%. Expected counts also appear: if a spinner lands on red with probability 1/4 and is spun 60 times, the expected number of red results is (1/4) * 60 = 15.
Two-way tables add one more skill: read the row total and column total carefully, because a conditional probability such as 'given the person is a student' uses only that row as the denominator, not the grand total of the whole table.
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?