The hardest part of most statistics word problems isn’t the math — it’s the translation. If you can turn the story into a clean “given/asked” setup, the calculations (mean, median, z-score, probability) become straightforward.
Want a clean setup from the story?
Paste the prompt into our ai math solver to get the formulas, substitutions, and a final sentence in context.
For almost any statistics word problem, start by writing this mini-template on your paper:
This prevents the most common error: doing a correct calculation for the wrong question.
Word problems often hide the math behind everyday language. Use this quick “dictionary” when you translate.
One underrated skill: decide whether you are working with a raw list of values (compute directly) or adistribution model (normal, binomial, etc.). The phrase “normally distributed” is a huge signal that you should switch from list-based calculations to z-scores/probabilities.
Keywords: average, typical, middle, most common. Tools: mean, median, mode.
Keywords: variability, consistency, spread. Tools: range, IQR, standard deviation.
Keywords: how unusual, compare across tests, above/below average. Tools: z-score.
Keywords: chance, likelihood, percentile, above/below, between. Tools: probability rules, normal CDF, z-table.
When a problem says “assume the distribution is normal,” that is a strong hint you’ll use z-scores and areas under the curve.
Problem: A student studies for 2, 3, 4, 1, and 5 hours over 5 days. What is the average time studied per day?
The word “average” signals mean.
Answer: The student studied an average of 3 hours per day.
Problem: The prices of 6 items are $8, $10, $10, $12, $100, and $120. Find the median price.
First, the list is already sorted. Because there are 6 values (even), the median is the average of the 3rd and 4th values.
Interpretation: Half the prices are below $11 and half are above. Notice how the outliers ($100 and $120) do not affect the median much.
Problem: SAT scores are normally distributed with mean μ = 1050 and standard deviation σ = 200. A student scored 1450. How unusual is this score?
“How unusual” is code for a z-score.
A z-score of 2 means the score is 2 standard deviations above the mean — definitely above average. If the question also asked for percentile, you would convert z = 2 into an area under the curve.
Many word problems ask you to compare “which group is more consistent” or “which set has more variability.” That is a spread question. The most common spread measure in intro stats is standard deviation.
Rule of thumb: larger standard deviation → values are more spread out → less consistent. smaller standard deviation → values cluster closer to the mean → more consistent.
If you are given two groups with the same mean but different standard deviations, the group with the smaller standard deviation has more predictable results.
Problem: A multiple-choice quiz has 10 questions with 4 options each. If you guess on every question, what is the probability you get exactly 7 correct?
This is a probability model. Each question is a trial with probability p = 1/4 of being correct. The phrase “exactly 7 correct” hints at a binomial-style setup.
A full solution uses combinations to count how many ways to choose which 7 questions are correct, then multiplies by probabilities. If you want a reference that connects word problems to probability rules and counting ideas, the OpenStax section on probability and counting rules is a helpful companion.
The key translation skill here is recognizing: “guessing” → fixed probability per trial, “exactly” → choose positions, and “independent questions” → multiply probabilities.
Teachers often grade statistics word problems for interpretation, not just arithmetic. Use these sentence templates so your answer matches the story.
If you can’t write a final sentence, it usually means you’re not sure what the number represents.
Tip: for #2, the outliers pull the mean; the median stays resistant. For #4, think about sample size and variability.
Start by identifying what the problem asks. Many errors come from computing the mean when the question wants the median.
In word problems, your final answer should be a sentence with units, not just a number.
Mean and standard deviation both depend on n. Count how many data values there are.
If the problem says “assume normal,” use z-scores/areas. If it is just a list of values, use mean/median/mode.
Paste your word problem and get the exact setup plus a clear final sentence.
Try AI Math Solver →