Learn how to solve GED statistics and probability questions involving mean, median, mode, range, weighted averages, missing values, outliers, frequency tables, and simple and compound events.
Quick Answer
Statistics questions ask you to organize, calculate, and interpret data.
Probability questions ask you to determine how likely an event is to happen.
For the GED Mathematical Reasoning test, you should know how to:
- Calculate mean, median, mode, and range
- Find a missing value when the mean is known
- Calculate a weighted average
- Understand how outliers affect data
- Select the most useful measure of center
- Read frequency tables and data displays
- Calculate the probability of a simple event
- Calculate the probability of compound events
- Distinguish independent from dependent events
- Use complements to find probability
- Interpret probability in real-world situations
These are part of the official GED Mathematical Reasoning content specifications.
The calculations are usually manageable. The harder part is deciding which calculation the question requires and interpreting what the result means.
Statistics Vocabulary You Must Understand
A data set is a collection of values.
For example:
4, 7, 7, 9, 13
Each number is a data value.
Statistics questions may ask you to summarize this set using:
- Mean
- Median
- Mode
- Range
These measurements describe different features of the same data. They are not interchangeable.
Mean
The mean is what most people call the average.
To calculate the mean:
- Add all the values.
- Divide the total by the number of values.
The official GED formula materials define the mean as the total of the values divided by the number of elements in the data set.
Example
Find the mean of:
6, 8, 10, 12, 14
Add the values:
6 + 8 + 10 + 12 + 14 = 50
There are five values:
50 ÷ 5 = 10
The mean is 10.
The Most Common Mean Mistake
Students sometimes divide by the wrong number.
You divide by the number of data values, not by:
- The largest value
- The number of different values
- The range
- The final value in the list
Example
Find the mean of:
3, 3, 6, 8
The total is:
3 + 3 + 6 + 8 = 20
There are four values, even though 3 appears twice.
20 ÷ 4 = 5
The mean is 5.
Repeated values must each be counted.
Median
The median is the middle value after the data has been arranged in numerical order.
Ordering the values is essential.
Odd Number of Values
Find the median of:
2, 11, 5, 8, 4
First, put the values in order:
2, 4, 5, 8, 11
The middle value is 5.
The median is 5.
Even Number of Values
When there is an even number of values, find the mean of the two middle values.
Find the median of:
3, 7, 9, 15
The middle values are 7 and 9.
7 + 9 = 16
16 ÷ 2 = 8
The median is 8.
The GED formula materials explain that the median is the middle ordered value or the mean of the two middle values when the set has an even number of values.
The Most Common Median Mistake
Students choose the number physically written in the middle before ordering the data.
For example:
12, 3, 20, 8, 9
The value written in the middle is 20, but 20 is not the median.
Order the values:
3, 8, 9, 12, 20
The median is 9.
Mode
The mode is the value that appears most frequently.
Example
Find the mode:
4, 6, 6, 7, 9
The number 6 appears twice. Every other value appears once.
The mode is 6.
More Than One Mode
A data set can have more than one mode.
Example
2, 2, 4, 5, 5, 8
Both 2 and 5 appear twice.
The set is bimodal, with modes of 2 and 5.
No Mode
A data set has no mode when no value appears more frequently than the others.
Example
3, 6, 8, 11
Every value appears once.
There is no mode.
The mode is not zero. It simply does not exist for this set.
Range
The range measures the spread between the highest and lowest values.
To calculate range:
Highest value − lowest value
Example
Find the range:
5, 8, 12, 17, 20
20 − 5 = 15
The range is 15.
The Most Common Range Mistake
Students count how many values are in the set.
Range does not tell you the number of values.
It tells you how far apart the lowest and highest values are.
For:
4, 6, 9, 13
The range is:
13 − 4 = 9
It is not 4 just because there are four values.
Mean, Median, Mode and Range in One Data Set
Consider this set:
2, 4, 4, 6, 9
Mean
2 + 4 + 4 + 6 + 9 = 25
25 ÷ 5 = 5
Mean = 5
Median
The values are already ordered.
The middle value is 4.
Median = 4
Mode
The most frequent value is 4.
Mode = 4
Range
9 − 2 = 7
Range = 7
One data set can produce four different answers because each measurement describes something different.
Choosing the Best Measure of Center
The mean, median, and mode are measures of central tendency.
A GED question may ask which one best represents a particular data set.
The correct choice depends on the data and the situation.
When the Mean Is Useful
The mean is useful when:
- All values should influence the result.
- The data does not contain an extreme outlier.
- You want a general numerical average.
Examples include:
- Average test score
- Average daily temperature
- Average number of products sold
- Average hours worked
When the Median Is More Useful
The median is often more representative when the data includes an unusually high or low value.
Examples include:
- Home prices
- Salaries
- Rent
- Household income
Example
Five employees earn:
$30,000, $32,000, $34,000, $36,000 and $250,000
The mean is:
330,000 ÷ 5 = 66,000
The mean salary is $66,000.
However, four of the five employees earn $36,000 or less.
The median is $34,000, which better represents the typical employee’s salary.
When the Mode Is Useful
The mode is useful when you need the most common value or category.
Examples include:
- Most commonly purchased shoe size
- Most popular product
- Most frequent survey response
- Most common test score
The mode can also be used with categories that cannot be meaningfully averaged.
For example, a store can identify its most popular shirt color using the mode, but it cannot calculate the mean color.
Outliers
An outlier is a value that is unusually distant from the rest of the data.
Example
10, 11, 12, 12, 13, 72
The value 72 is an outlier.
Outliers can greatly change the mean.
They usually have less effect on the median.
How an Outlier Affects the Mean
Without 72:
10 + 11 + 12 + 12 + 13 = 58
58 ÷ 5 = 11.6
With 72:
10 + 11 + 12 + 12 + 13 + 72 = 130
130 ÷ 6 ≈ 21.7
One extreme value raises the mean from 11.6 to approximately 21.7.
How an Outlier Affects the Median
Without 72, the median is 12.
With 72, the two middle values are still 12 and 12.
The median remains 12.
Recognition Shortcut
When a data set contains an extreme outlier:
- Expect the mean to change.
- Expect the median to remain more stable.
Finding a Missing Value When the Mean Is Known
The GED may provide the mean and all but one value, then ask you to find the missing value. This skill is included in official GED performance descriptors.
Example
The mean of five test scores is 82.
Four scores are:
78, 80, 85 and 88
What is the fifth score?
Step 1: Find the Required Total
Mean × number of values = total
82 × 5 = 410
The five scores must total 410.
Step 2: Add the Known Values
78 + 80 + 85 + 88 = 331
Step 3: Subtract
410 − 331 = 79
The missing score is 79.
Missing-Value Shortcut
When the mean and number of values are given:
- Multiply the mean by the number of values.
- Add the known values.
- Subtract the known total from the required total.
Do not simply average the values you already have. The question is asking you to reconstruct the complete data set.
Weighted Average
A weighted average is used when some values contribute more to the final result than others.
Official GED performance descriptors include calculating weighted averages.
Example
A course grade is based on:
- Homework: 20%
- Midterm: 30%
- Final exam: 50%
A student earns:
- Homework: 90
- Midterm: 80
- Final exam: 70
Multiply each score by its weight:
90 × 0.20 = 18
80 × 0.30 = 24
70 × 0.50 = 35
Add the weighted scores:
18 + 24 + 35 = 77
The weighted average is 77.
Weighted-Average Mistakes
Students commonly:
- Add the scores and divide by three.
- Use percentages as whole numbers instead of decimals.
- Forget that the weights should total 100%.
- Apply the wrong weight to a value.
- Round each step too early.
In the example above, a regular mean would be 80, but the weighted average is 77 because the lowest score carries the greatest weight.
Frequency Tables
A frequency table shows how often each value or category occurs.
Example
| Number of Books Read | Frequency |
|---|---|
| 0 | 2 |
| 1 | 5 |
| 2 | 4 |
| 3 | 1 |
This table shows:
- Two people read zero books.
- Five people read one book.
- Four people read two books.
- One person read three books.
Finding the Total Frequency
Add the frequency column:
2 + 5 + 4 + 1 = 12
The table represents 12 people.
Do not add the book values to find the number of people.
Finding the Mode From a Frequency Table
The highest frequency is 5.
That frequency corresponds to one book.
The mode is 1 book.
Finding the Mean From a Frequency Table
Multiply each value by its frequency.
0 × 2 = 0
1 × 5 = 5
2 × 4 = 8
3 × 1 = 3
Add the products:
0 + 5 + 8 + 3 = 16
Divide by the total frequency:
16 ÷ 12 ≈ 1.33
The mean is approximately 1.33 books.
Misleading Data Displays
Statistics questions may test whether a graph or chart creates a misleading impression.
A display can mislead readers through:
- A vertical axis that does not start at zero
- Unequal scale intervals
- Missing labels
- Different-sized images used to represent values
- Selective time periods
- Categories with unclear definitions
Example
A graph compares sales of 98 units and 102 units.
If the vertical axis begins at 97 rather than zero, the difference may appear enormous even though sales increased by only four units.
Always inspect:
- The title
- Axis labels
- Scale
- Units
- Time period
- Source of the data
Correlation Does Not Prove Causation
Two variables may move together without one causing the other.
Example
During summer, both ice cream sales and sunburn cases increase.
Ice cream does not cause sunburn.
Both increase because of another factor: hotter, sunnier weather.
Official GED performance descriptions include distinguishing correlation from causation.
Recognition Shortcut
- Correlation: Two variables are related.
- Causation: A change in one variable directly produces a change in the other.
A graph showing association is not enough by itself to prove causation.
Probability
Probability measures how likely an event is to occur.
A probability can be expressed as:
- A fraction
- A decimal
- A percentage
The probability of an impossible event is 0.
The probability of a certain event is 1, or 100%.
All probabilities fall between 0 and 1.
Probability of a Simple Event
For outcomes that are equally likely:
Probability = favorable outcomes ÷ total possible outcomes
The official GED assessment guide includes determining probabilities of simple and compound events.
Example
A bag contains:
- 3 red marbles
- 5 blue marbles
- 2 green marbles
There are 10 marbles in total.
The probability of selecting a red marble is:
3 ÷ 10 = 3/10
As a decimal:
0.3
As a percentage:
30%
Probability of Rolling a Number
A standard number cube has six equally likely outcomes:
1, 2, 3, 4, 5, 6
Example
What is the probability of rolling a 4?
There is one favorable outcome out of six possible outcomes.
Probability = 1/6
Probability of Rolling an Even Number
The even numbers are:
2, 4 and 6
There are three favorable outcomes.
3/6 = 1/2
The probability is 1/2, 0.5, or 50%.
Probability of Drawing From a Deck
A standard deck contains 52 cards.
There are:
- Four suits
- Thirteen cards in each suit
- Four aces
- Twenty-six red cards
- Twenty-six black cards
Example
What is the probability of drawing an ace?
4/52 = 1/13
The probability is 1/13.
Always simplify the fraction when possible.
Complementary Events
The complement of an event is everything that does not belong to that event.
The probabilities of an event and its complement add to 1.
P(not A) = 1 − P(A)
Example
The probability that it rains is 0.35.
The probability that it does not rain is:
1 − 0.35 = 0.65
The probability is 0.65, or 65%.
Using the Complement Shortcut
A question may ask for the probability of getting at least one particular result.
It is often easier to calculate the probability of getting none, then subtract from 1.
Example
A coin is flipped twice.
What is the probability of getting at least one head?
The possible outcomes are:
- HH
- HT
- TH
- TT
Three outcomes contain at least one head.
The answer is 3/4.
You can also use the complement:
Probability of no heads = probability of TT = 1/4
1 − 1/4 = 3/4
Independent Events
Events are independent when the result of one event does not change the probability of the next.
Examples include:
- Flipping a coin twice
- Rolling a number cube twice
- Spinning a spinner and then rolling a number cube
For independent events involving “and,” multiply the probabilities.
Example
What is the probability of flipping heads and then rolling a 6?
Probability of heads = 1/2
Probability of rolling a 6 = 1/6
Multiply:
1/2 × 1/6 = 1/12
The probability is 1/12.
Dependent Events
Events are dependent when the first event changes the probability of the next event.
This commonly happens when an item is selected and not replaced.
Example
A bag contains three red marbles and two blue marbles.
What is the probability of selecting two red marbles without replacement?
Probability of the first red marble:
3/5
After one red marble is removed, two red marbles remain out of four total marbles.
Probability of the second red marble:
2/4
Multiply:
3/5 × 2/4 = 6/20 = 3/10
The probability is 3/10.
With Replacement vs. Without Replacement
This wording changes the problem.
With Replacement
The first selected item is returned.
The total number of items and probabilities remain the same.
The events are generally independent.
Without Replacement
The selected item is not returned.
The total number of items changes.
The events are dependent.
Exam Trap
Never reuse the original denominator after an item has been removed without replacement.
“And” Probability Questions
When both events must happen, the question often uses the word and.
For independent or sequential events, multiply the probabilities.
Example
What is the probability of rolling an even number and then flipping tails?
Probability of an even number = 3/6 = 1/2
Probability of tails = 1/2
1/2 × 1/2 = 1/4
The probability is 1/4.
“Or” Probability Questions
When either event may happen, the question often uses the word or.
For mutually exclusive events, add the probabilities.
Mutually exclusive events cannot happen at the same time during one trial.
Example
What is the probability of rolling a 2 or a 5 on one number cube?
Probability of rolling a 2 = 1/6
Probability of rolling a 5 = 1/6
Add:
1/6 + 1/6 = 2/6 = 1/3
The probability is 1/3.
Overlapping Events
Some “or” events overlap.
In those cases, adding both probabilities counts the overlap twice.
Use:
P(A or B) = P(A) + P(B) − P(A and B)
Example
A card is drawn from a standard deck.
What is the probability of drawing a heart or a king?
There are:
- 13 hearts
- 4 kings
- 1 card that is both a heart and a king
Favorable outcomes:
13 + 4 − 1 = 16
Probability:
16/52 = 4/13
Subtracting the king of hearts prevents it from being counted twice.
Theoretical Probability
Theoretical probability is based on the expected mathematical outcomes.
Example
The theoretical probability of flipping heads on a fair coin is:
1/2, or 50%
This result comes from the two equally likely outcomes, not from performing an experiment.
Experimental Probability
Experimental probability is based on actual results.
Experimental probability = number of times the event occurred ÷ total trials
Example
A coin is flipped 40 times and lands on heads 17 times.
Experimental probability:
17/40 = 0.425
The experimental probability is 42.5%.
Why Experimental and Theoretical Probability May Differ
A fair coin has a theoretical probability of 50% for heads.
However, it may not land on heads exactly five times in ten flips.
With more trials, the experimental result often moves closer to the theoretical probability, but a perfect match is not guaranteed.
Expected Value From Probability
Some questions ask how many times an event is expected to happen.
Multiply the probability by the number of trials.
Example
The probability of winning a game is 0.30.
If the game is played 80 times, how many wins are expected?
0.30 × 80 = 24
Approximately 24 wins are expected.
This does not guarantee exactly 24 wins. It is a long-run expectation.
Common GED Statistics Mistakes
Students often:
- Find the median without ordering the data.
- Divide the mean by the wrong number.
- Confuse range with the number of values.
- Assume every data set has a mode.
- Ignore repeated values.
- Use the mean when an outlier makes the median more representative.
- Treat correlation as proof of causation.
- Read the wrong row or column of a frequency table.
- Ignore the graph’s scale.
- Round too early.
Common GED Probability Mistakes
Students often:
- Reverse favorable and total outcomes.
- Forget to count the total outcomes.
- Add probabilities when they should multiply.
- Multiply probabilities when they should add.
- Ignore whether an item is replaced.
- Keep the denominator unchanged after a selection without replacement.
- Count overlapping outcomes twice.
- Give an answer greater than 1 or 100%.
- Confuse theoretical probability with experimental results.
A Reliable Statistics Strategy
Use this process:
Step 1: Identify What the Question Wants
Does it ask for:
- Mean
- Median
- Mode
- Range
- Weighted average
- Missing value
- Best measure of center
- Interpretation of data
Step 2: Organize the Data
Place values in order when working with median, range, or outliers.
Step 3: Write the Required Operation
For example:
- Mean = total ÷ number of values
- Range = highest − lowest
- Required total = mean × number of values
Step 4: Calculate Carefully
Keep repeated values and frequencies in the calculation.
Step 5: Interpret the Result
Check whether the answer makes sense in the context of the question.
A Reliable Probability Strategy
Step 1: Identify the Event
What outcome must occur?
Step 2: Count All Possible Outcomes
Find the denominator.
Step 3: Count Favorable Outcomes
Find the numerator.
Step 4: Look for Important Wording
Watch for:
- And
- Or
- At least one
- With replacement
- Without replacement
- Independent
- Experimental
Step 5: Calculate
Multiply, add, subtract an overlap, or use a complement as required.
Step 6: Check the Answer
A probability cannot be less than 0 or greater than 1.
Real GED Example: Choosing the Best Average
Five homes sold for:
$180,000, $185,000, $190,000, $195,000 and $900,000
Which measure best represents the typical home price?
The $900,000 home is an extreme outlier.
The mean would be pulled upward and would not represent most of the homes.
The median is $190,000, making it the better measure of the typical price.
Real GED Example: Missing Score
A student’s mean score on four quizzes is 85.
The first three scores are:
82, 79 and 91
What is the fourth score?
Required total:
85 × 4 = 340
Known total:
82 + 79 + 91 = 252
Missing score:
340 − 252 = 88
The fourth score is 88.
Real GED Example: Compound Probability
A spinner has four equal sections labeled A, B, C, and D.
A number cube is also rolled.
What is the probability of spinning A and rolling an even number?
Probability of A:
1/4
Probability of an even number:
3/6 = 1/2
Multiply:
1/4 × 1/2 = 1/8
The probability is 1/8.
Real GED Example: Without Replacement
A box contains:
- Four black pens
- Three blue pens
Two pens are selected without replacement.
What is the probability that both are blue?
First blue pen:
3/7
Second blue pen:
2/6
Multiply:
3/7 × 2/6 = 6/42 = 1/7
The probability is 1/7.
Frequently Asked Questions
Are statistics and probability tested on GED Math?
Yes. Official GED materials include mean, median, mode, range, weighted averages, missing data values, and probabilities of simple and compound events.
Is the mean formula provided on the GED?
The official GED formula materials include an explanation of the mean, and test-takers receive access to a mathematics formula sheet. You still need to recognize when and how to use the information.
What is the difference between mean and median?
The mean is the total divided by the number of values. The median is the middle value after the data is ordered.
Which average is best when there is an outlier?
The median is often more representative because an extreme value can significantly change the mean.
Can a data set have two modes?
Yes. Two values that share the highest frequency make the data set bimodal.
Can a data set have no mode?
Yes. A set has no mode when no value appears more frequently than the others.
What is the difference between independent and dependent events?
Independent events do not change each other’s probabilities. In dependent events, the first result changes the probability of the next event.
What does “without replacement” mean?
The selected item is not returned before the next selection. The total number of available items changes.
When should probabilities be multiplied?
Probabilities are commonly multiplied when multiple events must all occur, especially in questions using “and.”
When should probabilities be added?
Probabilities are commonly added when either of two mutually exclusive outcomes may occur in a question using “or.”
Key Takeaways
- Mean is the total divided by the number of values.
- Median is the middle value after the data is ordered.
- Mode is the most frequent value.
- Range is the highest value minus the lowest value.
- Outliers usually affect the mean more than the median.
- A missing value can be found by reconstructing the required total.
- Weighted averages account for values that contribute different amounts.
- Simple probability compares favorable outcomes with all possible outcomes.
- Multiply probabilities when multiple events must occur.
- Replacement determines whether sequential selections are independent or dependent.
- Use the complement to simplify many “at least one” questions.
- Correlation does not automatically prove causation.
- Always read data labels, units, scales, and question wording carefully.
Test Your GED Math Skills
Statistics and probability questions test whether you can calculate accurately, interpret data, and apply mathematical reasoning to real situations.
Take our full GED Practice Test to practice realistic questions covering statistics, probability, algebra, geometry, graphs, formulas, and word problems while identifying the skills you need to strengthen before test day.
