Grade: Grade 7 Subject: Mathematics Unit: Statistics Lesson: 4 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Word Problems: Statistics

Learn

Word problems require you to extract data from real-world scenarios and apply statistical reasoning. This lesson focuses on reading carefully, identifying what's being asked, and choosing the right statistical measure.

Problem-Solving Strategy

  1. Read the problem carefully - Identify the data values and what question is being asked
  2. Organize the data - Write out the numbers clearly, order if needed
  3. Choose the right measure - Mean, median, mode, range, MAD, or IQR
  4. Calculate - Show your work step by step
  5. Check your answer - Does it make sense in context?

Recognizing Key Phrases

  • "Average" or "typical" often means mean or median
  • "Most common" or "most frequent" means mode
  • "Spread" or "variability" means range, MAD, or IQR
  • "Consistent" or "reliable" relates to low variability
  • "Compare" often requires looking at multiple measures

Examples

Example 1: Sports Statistics

Problem: A soccer team scored the following goals in their last 8 games: 2, 1, 3, 0, 4, 2, 1, 3. The coach wants to know the team's typical scoring performance. Find the mean and median goals per game.

Solution:

Step 1: Sum = 2 + 1 + 3 + 0 + 4 + 2 + 1 + 3 = 16 goals

Step 2: Mean = 16 / 8 = 2 goals per game

Step 3: Ordered data: 0, 1, 1, 2, 2, 3, 3, 4

Step 4: Median = (2 + 2) / 2 = 2 goals (average of 4th and 5th values)

Answer: The team typically scores 2 goals per game (both mean and median are 2).

Example 2: Comparing Businesses

Problem: Restaurant A had daily customers: 45, 52, 48, 50, 55. Restaurant B had: 30, 40, 50, 60, 70. Both have the same mean (50 customers). Which restaurant has more predictable customer traffic?

Solution:

Restaurant A Range: 55 - 45 = 10 customers

Restaurant B Range: 70 - 30 = 40 customers

Answer: Restaurant A has more predictable customer traffic because its range (10) is much smaller than Restaurant B's range (40).

Example 3: Finding a Missing Value

Problem: Marcus needs an average of 85 on five tests to earn an A. His first four test scores are 82, 88, 79, and 90. What minimum score does he need on the fifth test?

Solution:

Step 1: Total points needed = 85 x 5 = 425 points

Step 2: Current total = 82 + 88 + 79 + 90 = 339 points

Step 3: Points needed = 425 - 339 = 86 points

Answer: Marcus needs at least 86 on his fifth test.

Practice

Solve these word problems. Show all your work and write your answer in context.

Problem 1: A delivery driver recorded these delivery times (in minutes) for one week: 25, 18, 32, 22, 28, 15, 30. What was the average delivery time? What was the range of delivery times?

Problem 2: The prices of laptops at a store are: $450, $520, $480, $1,200, $490, $510. A customer asks, "What's a typical laptop price here?" Should the salesperson report the mean or median? Calculate both and explain your choice.

Problem 3: A gardener measured plant heights (in cm) in two garden beds. Bed A: 15, 18, 16, 17, 19. Bed B: 12, 14, 18, 20, 21. Which bed has plants that are more uniform in height? Use range to support your answer.

Problem 4: Emma's bowling scores for 6 games are: 112, 125, 118, 130, 115, 122. She wants to increase her average to 125. What score does she need in her 7th game?

Problem 5: A survey asked students how many books they read last month: 0, 1, 1, 2, 2, 2, 3, 3, 4, 12. One student claims the typical student reads about 3 books. Another claims it's about 2 books. Who is using the mean? Who is using the median? Which is more representative?

Problem 6: Two factories produce light bulbs. Factory X's bulb lifetimes (in hours): 980, 1010, 995, 1005, 1020. Factory Y's lifetimes: 850, 950, 1000, 1050, 1150. Both have a mean of 1002 hours. Which factory produces more reliable bulbs? Explain using variability.

Problem 7: A shoe store tracked sales of shoe sizes for one day: 7, 8, 8, 9, 9, 9, 9, 10, 10, 11. What is the mode? Why is the mode the most useful measure for the store manager to know?

Problem 8: The ages of players on a youth basketball team are: 12, 12, 13, 13, 13, 14, 14, 14, 14, 15. Find the mean, median, and mode. Are these measures close to each other? What does that tell you about the data distribution?

Problem 9: A sample of 8 students reported study times (in hours per week): 5, 7, 8, 10, 12, 15, 18, ?. If the median study time is 11 hours, what are the possible values for the missing data point?

Problem 10: Company A employees earn: $35,000, $38,000, $40,000, $42,000, $45,000. Company B employees earn: $32,000, $36,000, $40,000, $44,000, $250,000 (CEO). A job seeker compares salaries. Which company has a higher mean salary? Which has a higher median? Which measure should the job seeker use to compare typical employee pay?

Check Your Understanding

Reflect on these questions before moving on.

  1. What key phrases in word problems signal you should find the mean?
  2. When would a store manager prefer to know the mode over the mean?
  3. How can outliers affect mean vs. median differently?
  4. What does it mean when we say one data set has more "variability" than another?
  5. How do you find a missing value when you know the desired average?

Next Steps

  • Practice translating word problems into mathematical calculations
  • Look for real-world statistics in news articles and analyze them
  • Move on to Common Mistakes to learn what errors to avoid