Chapter 6 · Lesson 5 of 12 · Grade 6 · Statistics & Probability · MAT-06-SP-005
Find Mean, Median, and Mode
Represent and solve find mean, median, and mode problems using precise mathematical notation, models, and reasoning.
Math V4 · Course chapter
Chapter 6: Statistics, Variability, and Mathematical Modeling
Using data and reasoning to support claims
Essential question: How can data, models, and mathematical arguments be used responsibly to describe variation and evaluate conclusions?
Where this lesson fits
Lesson 5 of 12. Each lesson builds on earlier chapter representations and ideas rather than resetting the topic.
Chapter destination
Collect a small data set, choose appropriate displays and summary measures, critique a misleading claim, and present a defensible conclusion.
Learning objectives
What you should be able to do
- Represent and solve find mean, median, and mode problems using precise mathematical notation, models, and reasoning.
- Explain why a method for find mean, median, and mode works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Chapter 6: Statistics, Variability, and Mathematical Modeling
Using data and reasoning to support claims. This is Lesson 5 of 12 in Chapter 6. It builds on earlier chapter ideas instead of restarting the topic from scratch.
Connection to the course
Cumulative knowledge used here includes all previous chapters. As you work, connect today's idea to earlier lessons in the chapter and keep those earlier representations available for comparison.
Mathematical meaning
Find Mean, Median, and Mode describes data or chance while accounting for variability. Calculations must be interpreted in the context of data collection or a probability model.
Represent the relationship
The Math Box uses statistics plot to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify calculations from the raw values, then decide whether the sample, display, center, spread, or probability model actually supports the claim.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Statistics Lab
Change the data and watch center and spread respond.
- Model one example of find mean, median, and mode in the Math Box.
- Change one input, predict the effect, and test the prediction.
- Connect the model to another representation used earlier in this chapter.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
Find the mean of 2, 4, 5, 7, 7, 9.
34 ÷ 6 = 5.67The mean redistributes the total equally.
Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: Find the mean of 3, 5, 6, 8, 8, 10.
40 ÷ 6 = 6.67The representation should show the same mathematical relationship as the calculation. The mean redistributes the total equally.
Explain why a valid method works, then solve: Find the mean of 4, 6, 7, 9, 9, 11.
46 ÷ 6 = 7.67A complete explanation names the relationship or property being preserved. The mean redistributes the total equally.
Estimate or predict first, then calculate and decide whether the result is reasonable: Find the mean of 5, 7, 8, 10, 10, 12.
52 ÷ 6 = 8.67The estimate is a reasonableness check, not a replacement for the exact result. The mean redistributes the total equally.
Solve and verify the result with a second method, inverse operation, or equivalent representation: Find the mean of 6, 8, 9, 11, 11, 13.
58 ÷ 6 = 9.67Verification should independently support the result. The mean redistributes the total equally.
Interpret the answer in context after solving. What does the result mean here? Find the mean of 7, 9, 10, 12, 12, 14.
64 ÷ 6 = 10.67State the result with its meaning, units, direction, or comparison—not only a number. The mean redistributes the total equally.
Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: Find the mean of 8, 10, 11, 13, 13, 15.
Interpret center with spread, shape, and sampling method. Correct solution: 70 ÷ 6 = 11.67Error analysis requires identifying the broken idea, not merely replacing the final answer. The mean redistributes the total equally.
Compare two related cases and explain what changes and what stays mathematically consistent. Case A: Find the mean of 9, 11, 12, 14, 14, 16. Case B: Find the mean of 18, 20, 21, 23, 23, 25.
Case A: 76 ÷ 6 = 12.67 Case B: 130 ÷ 6 = 21.67Compare the structure, representation, units, and result rather than only the numbers. The mean redistributes the total equally.
Find the mean of 10, 12, 13, 15, 15, 17.
82 ÷ 6 = 13.67The mean redistributes the total equally.
Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: Find the mean of 11, 13, 14, 16, 16, 18.
88 ÷ 6 = 14.67The representation should show the same mathematical relationship as the calculation. The mean redistributes the total equally.
Explain why a valid method works, then solve: Find the mean of 12, 14, 15, 17, 17, 19.
94 ÷ 6 = 15.67A complete explanation names the relationship or property being preserved. The mean redistributes the total equally.
Estimate or predict first, then calculate and decide whether the result is reasonable: Find the mean of 13, 15, 16, 18, 18, 20.
100 ÷ 6 = 16.67The estimate is a reasonableness check, not a replacement for the exact result. The mean redistributes the total equally.
Solve and verify the result with a second method, inverse operation, or equivalent representation: Find the mean of 14, 16, 17, 19, 19, 21.
106 ÷ 6 = 17.67Verification should independently support the result. The mean redistributes the total equally.
Interpret the answer in context after solving. What does the result mean here? Find the mean of 15, 17, 18, 20, 20, 22.
112 ÷ 6 = 18.67State the result with its meaning, units, direction, or comparison—not only a number. The mean redistributes the total equally.
Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: Find the mean of 16, 18, 19, 21, 21, 23.
Interpret center with spread, shape, and sampling method. Correct solution: 118 ÷ 6 = 19.67Error analysis requires identifying the broken idea, not merely replacing the final answer. The mean redistributes the total equally.
Compare two related cases and explain what changes and what stays mathematically consistent. Case A: Find the mean of 17, 19, 20, 22, 22, 24. Case B: Find the mean of 26, 28, 29, 31, 31, 33.
Case A: 124 ÷ 6 = 20.67 Case B: 178 ÷ 6 = 29.67Compare the structure, representation, units, and result rather than only the numbers. The mean redistributes the total equally.
Find the mean of 18, 20, 21, 23, 23, 25.
130 ÷ 6 = 21.67The mean redistributes the total equally.
Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: Find the mean of 19, 21, 22, 24, 24, 26.
136 ÷ 6 = 22.67The representation should show the same mathematical relationship as the calculation. The mean redistributes the total equally.
Explain why a valid method works, then solve: Find the mean of 20, 22, 23, 25, 25, 27.
142 ÷ 6 = 23.67A complete explanation names the relationship or property being preserved. The mean redistributes the total equally.
Estimate or predict first, then calculate and decide whether the result is reasonable: Find the mean of 21, 23, 24, 26, 26, 28.
148 ÷ 6 = 24.67The estimate is a reasonableness check, not a replacement for the exact result. The mean redistributes the total equally.
Practice
Guided practice with hints
01Solve and verify the result with a second method, inverse operation, or equivalent representation: Find the mean of 22, 24, 25, 27, 27, 29.
Hint: Choose a representation before computing.
Answer: 154 ÷ 6 = 25.67
02Interpret the answer in context after solving. What does the result mean here? Find the mean of 23, 25, 26, 28, 28, 30.
Hint: Explain what relationship or property makes your method valid.
Answer: 160 ÷ 6 = 26.67
03Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: Find the mean of 24, 26, 27, 29, 29, 31.
Hint: Choose a representation before computing.
Answer: Interpret center with spread, shape, and sampling method. Correct solution: 166 ÷ 6 = 27.67
04Compare two related cases and explain what changes and what stays mathematically consistent. Case A: Find the mean of 25, 27, 28, 30, 30, 32. Case B: Find the mean of 34, 36, 37, 39, 39, 41.
Hint: Explain what relationship or property makes your method valid.
Answer: Case A: 172 ÷ 6 = 28.67 Case B: 226 ÷ 6 = 37.67
05Find the mean of 26, 28, 29, 31, 31, 33.
Hint: Choose a representation before computing.
Answer: 178 ÷ 6 = 29.67
06Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: Find the mean of 27, 29, 30, 32, 32, 34.
Hint: Explain what relationship or property makes your method valid.
Answer: 184 ÷ 6 = 30.67
Practice
Independent practice
01Explain why a valid method works, then solve: Find the mean of 28, 30, 31, 33, 33, 35.
Answer: 190 ÷ 6 = 31.67
02Estimate or predict first, then calculate and decide whether the result is reasonable: Find the mean of 29, 31, 32, 34, 34, 36.
Answer: 196 ÷ 6 = 32.67
03Solve and verify the result with a second method, inverse operation, or equivalent representation: Find the mean of 30, 32, 33, 35, 35, 37.
Answer: 202 ÷ 6 = 33.67
04Interpret the answer in context after solving. What does the result mean here? Find the mean of 31, 33, 34, 36, 36, 38.
Answer: 208 ÷ 6 = 34.67
05Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: Find the mean of 32, 34, 35, 37, 37, 39.
Answer: Interpret center with spread, shape, and sampling method. Correct solution: 214 ÷ 6 = 35.67
06Compare two related cases and explain what changes and what stays mathematically consistent. Case A: Find the mean of 33, 35, 36, 38, 38, 40. Case B: Find the mean of 42, 44, 45, 47, 47, 49.
Answer: Case A: 220 ÷ 6 = 36.67 Case B: 274 ÷ 6 = 45.67
07Find the mean of 34, 36, 37, 39, 39, 41.
Answer: 226 ÷ 6 = 37.67
08Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: Find the mean of 35, 37, 38, 40, 40, 42.
Answer: 232 ÷ 6 = 38.67
Common mistakes
Learn to catch the error, not just the answer.
Interpret center with spread, shape, and sampling method.
Finite experimental frequencies vary even when a model is correct.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Summarize data, compare groups, evaluate survey claims, and describe uncertainty.
- Build probability models and simulations for repeated random processes.
Challenge problems
Explain why a valid method works, then solve: Find the mean of 36, 38, 39, 41, 41, 43.
238 ÷ 6 = 39.67
Estimate or predict first, then calculate and decide whether the result is reasonable: Find the mean of 37, 39, 40, 42, 42, 44.
244 ÷ 6 = 40.67
Solve and verify the result with a second method, inverse operation, or equivalent representation: Find the mean of 38, 40, 41, 43, 43, 45.
250 ÷ 6 = 41.67
Interpret the answer in context after solving. What does the result mean here? Find the mean of 39, 41, 42, 44, 44, 46.
256 ÷ 6 = 42.67
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 6 Chapter 6 Reasoning Lab
Solve find mean, median, and mode problems accurately, choose an appropriate representation, and justify each result with a check.
Practice
Mastery check
01Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: Find the mean of 40, 42, 43, 45, 45, 47.
Answer: Interpret center with spread, shape, and sampling method. Correct solution: 262 ÷ 6 = 43.67
02Compare two related cases and explain what changes and what stays mathematically consistent. Case A: Find the mean of 41, 43, 44, 46, 46, 48. Case B: Find the mean of 50, 52, 53, 55, 55, 57.
Answer: Case A: 268 ÷ 6 = 44.67 Case B: 322 ÷ 6 = 53.67
03Find the mean of 42, 44, 45, 47, 47, 49.
Answer: 274 ÷ 6 = 45.67
04Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: Find the mean of 43, 45, 46, 48, 48, 50.
Answer: 280 ÷ 6 = 46.67
05Explain why a valid method works, then solve: Find the mean of 44, 46, 47, 49, 49, 51.
Answer: 286 ÷ 6 = 47.67
06Estimate or predict first, then calculate and decide whether the result is reasonable: Find the mean of 45, 47, 48, 50, 50, 52.
Answer: 292 ÷ 6 = 48.67
07Solve and verify the result with a second method, inverse operation, or equivalent representation: Find the mean of 46, 48, 49, 51, 51, 53.
Answer: 298 ÷ 6 = 49.67
08Interpret the answer in context after solving. What does the result mean here? Find the mean of 47, 49, 50, 52, 52, 54.
Answer: 304 ÷ 6 = 50.67
Terminology
Words to know
- distribution
- The pattern of values including center, spread, shape, and unusual features.
- variability
- The degree to which observations differ.
- sample
- A subset of a population used to collect information.
- probability
- A number from 0 to 1 describing likelihood.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
Grade 6 scope, sequence, standards, and public task structure
Reference for coherent sequencing, representations, dependency-aware progression, and reasoning-rich task types.Eureka Math² Grade 6 program structure
Reference for module/topic coherence, recap, mixed-practice, and cumulative-learning patterns.enVision Mathematics Grade 6 instructional model
Reference for problem-based entry points, visual learning, modeling, and application patterns.Common Core State Standards for Mathematics — Grade 6
Grade-level content and mathematical-practice expectations.