GED SCIENCE • SCIENCE PRACTICES

Apply Probability and Statistics in Scientific Contexts

Learn to interpret means, ranges, probabilities, and data patterns the way scientists do.

Why Scientists Need Probability and Statistics

Science is built on observation, but observations can be messy. Two patients might respond differently to the same medicine. Two weather stations might record different temperatures on the same day. Probability and statistics give scientists the tools to cut through that messiness, find real patterns, and make confident conclusions. Without these tools, we would have no way to tell whether a new drug actually works or whether a crop really grows better with a certain fertilizer.

1654
Birth of Probability Theory
Blaise Pascal and Pierre de Fermat exchange letters about games of chance, laying the mathematical foundations for probability.
1809
The Normal Distribution
Carl Friedrich Gauss describes the bell-shaped curve, showing that measurement errors and natural variation often follow a predictable pattern.
1900s
Statistics Meets Medicine
Researchers begin using controlled clinical trials with statistical analysis to test drugs and vaccines, transforming modern healthcare.
2020s
Data-Driven Science Today
From climate modeling to genomics, virtually every field of science relies on probability and statistics to analyze massive datasets and draw evidence-based conclusions.

On the GED Science test, you will not be asked to perform complex statistical calculations. Instead, you will be asked to interpret data presented in tables, graphs, and passages — and to use basic ideas like averages, ranges, and probability to evaluate scientific claims. The big question this lesson addresses is: How do you look at a set of numbers and figure out what they are really telling you?

Core Principles of Probability and Statistics

Before we dive into calculations, let's establish the key ideas you will encounter on the GED. These concepts appear again and again, whether the topic is biology, chemistry, earth science, or physics.

1

Mean (Average)

Add all values together, then divide by the number of values. The mean tells you the central tendency — the typical value in a dataset.
2

Median

The middle value when all data points are arranged from smallest to largest. The median is less affected by extreme outliers than the mean.
3

Range

The difference between the highest and lowest values. A large range means the data are spread out; a small range means they are clustered together.
4

Probability

The likelihood that an event will happen, expressed as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain).
5

Sample Size

The number of observations or trials in a study. Larger samples produce more reliable results because they reduce the impact of random variation.
KEY TAKEAWAY
Think of statistics like a camera lens. A single photo (one data point) might be blurry or taken at a bad angle. But if you take dozens of photos and stack them together, the true image — the real pattern — starts to come through clearly. Statistics is the process of stacking those photos.

Visualizing Data: Mean, Median, and Range

The diagram below shows the daily high temperatures recorded over one week at a weather station. It illustrates how we calculate the mean, median, and range from those seven data points.

The bar chart shows seven daily temperature readings. The dashed pink line marks the mean (≈ 74.6 °F), while the dashed violet line marks the median (75 °F). The range is 82.5 − 65 = 17.5 °F.

Notice how the mean and median are close together here. That happens when data are fairly symmetrical. If Sunday's temperature had been 40 °F instead of 65 °F (an extreme outlier), the mean would drop significantly, but the median would barely change. This is why scientists often report both values — the median resists being pulled by outliers.

The Math Behind the Concepts

The GED provides an on-screen calculator (TI-30XS), so you will not need to do heavy arithmetic by hand. However, understanding the formulas helps you know what the numbers mean and when to apply each one.

MEAN (AVERAGE)
Mean = (Sum of all values) ÷ (Number of values)
Example: (75 + 80 + 70 + 72.5 + 77.5 + 82.5 + 65) ÷ 7 = 522.5 ÷ 7 ≈ 74.6 °F
RANGE
Range = Maximum value − Minimum value
Example: 82.5 − 65 = 17.5 °F. A wider range means more variability in the data.
PROBABILITY
P(event) = (Number of favorable outcomes) ÷ (Total number of possible outcomes)
P ranges from 0 (impossible) to 1 (certain). Multiply by 100 to express as a percentage. Example: If 3 out of 10 seeds germinate, P(germination) = 3 ÷ 10 = 0.30, or 30%.
PERCENT CHANGE
Percent Change = [(New Value − Old Value) ÷ Old Value] × 100
Scientists use percent change to describe how much a measurement has increased or decreased relative to its starting point.
💡 GED TIP
You do not need to memorize these formulas for the test. They will usually be implied by the question. What matters most is understanding what each statistic tells you and being able to calculate it from a data table or graph when asked.

Probability in Science — From Genetics to Weather

Probability shows up across every branch of science. In genetics, we predict the likelihood that offspring will inherit a particular trait. In earth science, we discuss the probability of earthquakes or severe storms. In medicine, we evaluate how likely a treatment is to succeed. The diagram below shows one of the most common probability tools in biology: a Punnett square.

This Punnett square crosses two heterozygous parents (Bb × Bb). Each cell represents an equally likely outcome with a probability of 1/4, or 25%. Three of the four cells produce the brown-eye phenotype, so the probability of brown eyes is 3/4, or 75%.

On the GED, you might see a Punnett square and be asked: "What is the probability that offspring will have blue eyes?" The answer is found by counting favorable outcomes (1 out of 4 cells shows bb) and dividing by total outcomes (4). That gives 1/4 = 0.25 = 25%. Probability questions in other contexts — such as "What is the chance that a volcano will erupt in the next 50 years?" — follow the same logic of favorable outcomes divided by total outcomes, though the data source may be historical records rather than a genetic model.

Worked Example: Analyzing Experimental Data

Let's walk through a GED-style scenario step by step. Read the passage and data table below, then follow the analysis.

🔬 SCENARIO
A biologist tested a new plant fertilizer. She grew 5 plants with the fertilizer (Group A) and 5 plants without it (Group B) under identical conditions for 30 days. She measured plant height (cm) at the end of the experiment.
Plant heights (cm) after 30 days
Plant #Group A (Fertilizer)Group B (No Fertilizer)
124 cm18 cm
222 cm16 cm
326 cm19 cm
421 cm17 cm
527 cm15 cm
Calculating and Comparing Group Statistics
1
Step 1 — Calculate the Mean for Group AAdd all Group A values: 24 + 22 + 26 + 21 + 27 = 120. Divide by the number of plants: 120 ÷ 5 = 24.
Mean A = 24.0 cm
2
Step 2 — Calculate the Mean for Group BAdd all Group B values: 18 + 16 + 19 + 17 + 15 = 85. Divide by the number of plants: 85 ÷ 5 = 17.
Mean B = 17.0 cm
3
Step 3 — Compare the MeansThe difference is 24.0 − 17.0 = 7.0 cm. Plants in the fertilizer group grew an average of 7 cm taller, which suggests the fertilizer had a positive effect on growth.
Difference = 7.0 cm (Group A is taller)
4
Step 4 — Calculate the Range for Each GroupGroup A range: 27 − 21 = 6 cm. Group B range: 19 − 15 = 4 cm. Group A shows slightly more variation, but both groups have relatively small ranges, meaning the results are fairly consistent within each group.
Range A = 6 cm | Range B = 4 cm
5
Step 5 — Evaluate the ConclusionThe data support the claim that the fertilizer increased plant growth. However, with only 5 plants per group, the sample size is small, which limits how confident we can be. A scientist would recommend repeating the experiment with a larger sample to strengthen the conclusion.
Conclusion: Data support fertilizer's effectiveness, but sample size is a limitation.

Strengths and Common Pitfalls

Statistical tools are powerful, but they can be misused or misunderstood. On the GED, you may be asked to identify weaknesses in a study or explain why a conclusion is not fully supported. The table below summarizes what each statistical measure does well and where it falls short.

Strengths and pitfalls of common statistical tools
Statistical ToolStrengthCommon Pitfall
MeanUses all data points; easy to calculate and understand.Easily skewed by outliers. One extreme value can make the mean misleading.
MedianResistant to outliers; shows the true middle of the data.Does not reflect how spread out the values are above and below the middle.
RangeQuick snapshot of spread; very easy to calculate.Only considers two values (max and min). One outlier makes the range look much larger than the typical spread.
ProbabilityProvides a clear prediction of likelihood; essential for genetics and risk assessment.Predicts what should happen on average over many trials, not what will happen in any single case.
Sample SizeLarger samples increase reliability and confidence in results.A large sample with biased selection (e.g., only one age group) still produces unreliable conclusions.
KEY TAKEAWAY
Think of each statistical tool as a different type of flashlight. The mean shines a broad, even beam, but it can be blinded by a sudden bright spot (an outlier). The median shines a narrow beam straight at the middle, ignoring distractions at the edges. The range just measures how wide the room is from wall to wall. You need multiple flashlights to truly understand a dark room — and you need multiple statistics to truly understand a dataset.

Connecting to Broader Scientific Reasoning

The GED Science test does not ask you to perform advanced statistical tests, but it does expect you to understand the ideas behind them. In professional science, researchers go beyond means and ranges to use tools like standard deviation and statistical significance. Here is a quick comparison of what you need for the GED versus what scientists use in the field.

GED-level vs. advanced statistical reasoning
ConceptWhat You Need for the GEDWhat Scientists Use Beyond the GED
Measuring centerCalculate or interpret the mean and median.Use weighted means, geometric means, or mode depending on data distribution.
Measuring spreadCalculate or interpret the range.Calculate standard deviation and variance to describe how tightly data cluster around the mean.
Drawing conclusionsCompare group means and note sample size limitations.Run hypothesis tests (t-tests, chi-square) to determine if differences are statistically significant.
ProbabilityUse simple probability ratios (favorable / total).Apply Bayesian probability, conditional probability, and probability distributions.

The takeaway here is that the GED tests your foundational understanding — whether you can read a table, compute a basic statistic, and use it to evaluate a scientific claim. If you master the concepts in this lesson, you will have a strong base not only for the test, but for any future coursework in science, health, or social science.

Practice Problems

1
A researcher records the following test scores for a group of students: 70, 72, 74, 76, 98. She calculates a mean of 78 and a median of 74. A classmate says, "The average score is 78, so the typical student scored around 78." Which of the following best explains why this claim may be misleading?
2
A scientist measured the mass (in grams) of five rock samples: 12, 15, 18, 14, and 21. What is the range of the data?
3
In a genetics experiment, two heterozygous tall pea plants (Tt) are crossed. The Punnett square predicts that 25% of offspring should be short (tt). A student grows 40 offspring and finds that 14 are short (35%). Which of the following is the best explanation for the difference between the predicted and observed results?
PROBLEM 4APPLIED
A public health study tracked influenza cases in a city over four months: Month | Cases January | 320 February | 480 March | 210 April | 90 Using the data above, explain what the mean number of monthly cases is, describe the trend in the data, and discuss one limitation of using only the mean to summarize these data. Write your response in 3–5 sentences.
PROBLEM 5CRITICAL THINKING
Two agricultural researchers tested the same new herbicide on weed growth. Researcher A grew 10 plots with herbicide and 10 without. She found the mean weed count was 12 per plot with herbicide and 30 per plot without. Range for herbicide plots: 8–16. Range for control plots: 22–38. Researcher B grew 3 plots with herbicide and 3 without. He found the mean weed count was 11 per plot with herbicide and 28 per plot without. Range for herbicide plots: 4–20. Range for control plots: 15–45. Both researchers concluded that the herbicide significantly reduces weed growth. Using the data and statistical reasoning, evaluate which researcher's conclusion is better supported. In your response, reference at least two specific statistical concepts (such as mean, range, or sample size) and explain how they strengthen or weaken each conclusion. Write 4–7 sentences.

Lesson Summary

Probability and statistics are the tools scientists use to make sense of data. The mean (average) tells you the central value of a dataset, while the median reveals the true middle and resists being distorted by outliers. The range shows how spread out the data are, and probability quantifies the likelihood of an event as favorable outcomes divided by total outcomes.

On the GED Science test, remember that a larger sample size produces more reliable results. Always consider whether a study's data are consistent (small range) and whether the sample is large enough to support the conclusion. When you see a data table or graph, ask yourself: What is the pattern? What is the average telling me? Could an outlier be distorting the picture? These questions will guide you through nearly every statistics-based question on the exam.

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