Statistics Word Problems
Apply your statistics skills to solve real-world problems involving sports, money, science, and everyday situations.
Problem-Solving Strategy
Word problems require you to extract data from a story and decide which statistical measure to use. Follow this strategy to tackle any statistics word problem:
R.E.A.D. Strategy for Word Problems
R - Read the problem carefully. What information is given?
E - Extract the data. Write down the numbers.
A - Analyze what is being asked. Mean? Median? Mode? Range?
D - Do the calculation and check your answer makes sense.
- Mean: "average," "typical value," "per person/item"
- Median: "middle value," "half above/below," data with outliers
- Mode: "most common," "most popular," "most frequent"
- Range: "spread," "difference," "variation"
Worked Examples
1 Sports Statistics Mean
The school basketball team scored the following points in their last 6 games: 48, 52, 45, 61, 55, and 47. The coach wants to know the team's average points per game to report to the school newspaper.
What is the mean number of points the team scored per game?
Solution
2 Income Data Median vs Mean
A small company has 7 employees with the following annual salaries:
| Employee | Salary |
|---|---|
| Assistant 1 | $28,000 |
| Assistant 2 | $30,000 |
| Technician | $35,000 |
| Specialist | $42,000 |
| Manager | $55,000 |
| Director | $72,000 |
| CEO | $250,000 |
What is the median salary? Why might the median be a better measure than the mean for this data?
Solution
The median better represents a "typical" salary because the CEO's outlier salary pulls the mean much higher than what most employees earn.
3 Retail Data Mode
A clothing store manager is deciding which t-shirt sizes to order more of. Here are the sizes sold last week:
Sizes sold: M, L, M, S, L, M, XL, M, L, M, S, M, L, M, XL, L
What size should the manager order the most of? (Find the mode)
Solution
The manager should order more medium-sized shirts since they sell the most.
4 Weather Data Range
A meteorologist recorded the high temperatures (in degrees Fahrenheit) for a week in April:
Daily highs: 62, 58, 71, 65, 73, 68, 55
What is the range of temperatures? What does this tell us about the weather that week?
Solution
The temperature varied by 18 degrees throughout the week, showing typical spring weather variability.
Practice Problems
Solve these word problems on your own. Remember to use the R.E.A.D. strategy!
Problem 1: Science Experiment
A student measured the growth of a plant (in cm) over 5 days: 2.1, 2.5, 2.3, 2.8, 2.3. What was the mean daily growth?
Problem 2: Test Scores
Nine students took a math test. Their scores were: 78, 82, 95, 88, 72, 90, 85, 79, 91. What is the median score?
Problem 3: Restaurant Survey
A pizza restaurant asked customers to rate their service from 1-5. Results: 4, 5, 4, 3, 5, 4, 5, 4, 2, 4, 5, 4. What was the most common rating (mode)?
Problem 4: Running Times
Maria's 5K running times (in minutes) for her last 6 races were: 28, 31, 27, 29, 32, 27. What is the range of her times?
Problem 5: Allowance Money
Six friends compared their weekly allowances: $10, $15, $12, $10, $20, $11. What is the median allowance?
Problem 6: Movie Theater
A movie theater tracked attendance for 7 days: 145, 230, 180, 195, 310, 285, 175. What was the average (mean) daily attendance?
Problem 7: Spelling Bee
In a spelling bee, competitors were eliminated in these rounds: 3, 5, 2, 7, 5, 4, 5, 6, 5, 3. In which round were the most competitors eliminated?
Problem 8: Combined Analysis
A store sold these numbers of items each day: 42, 38, 55, 41, 38, 47, 52. Calculate the mean number of items sold per day (round to 1 decimal).
Check Your Understanding
Key Takeaways:
- Always read the problem carefully to identify what measure is needed
- Look for keywords: "average" = mean, "middle" = median, "most common" = mode
- Use median when data has outliers or extreme values
- The range tells you how spread out the data is
- Check that your answer makes sense in the context of the problem
Next Steps
- Practice creating your own word problems with data you collect
- Look for statistics in news articles and analyze them
- Move on to Common Mistakes to learn what errors to avoid