Level 2 · Enrichment

Reveal Math · Unit 2 · Supplemental

Statistics & Data

Grade 6 · Standards 6.SP.A.1–3, 6.SP.B.5 — analyzing distributions, outliers & data displays

Name: Date:

Challenge Problems

Directions: Solve and show your strategy. For each "Explain" prompt, write a complete sentence that justifies your reasoning with the data.
  1. A data set is 4, 6, 6, 8, 11. Add one value so that the mean becomes exactly 7. What value did you add? Reasoning
    Explain: how did you use the target total to find the missing value?
  2. The mean of 5 quiz scores is 88. Four of them are 90, 85, 92, 80. Find the fifth score. Multi-step
  3. Which changes more when a very large outlier is added to a data set — the mean or the median? Reasoning
    Explain why, using what each measure depends on.
  4. A data set has mean 10, median 10, and mode 10, with 5 values. Write one possible data set. Then write a different one. Open-ended
  5. Daily temperatures (°F): 72, 75, 68, 90, 71, 73. Find the mean and median. Which better represents a "typical" day, and why? Reasoning
    Explain your choice using the idea of an outlier.
  6. A histogram groups times into 0–9, 10–19, 20–29 min with frequencies 4, 10, 6. How many data points are there? Can you find the exact mean? Multi-step
    Explain why a histogram limits how precisely you can compute the mean.
  7. Two classes have the same mean test score, but Class A has range 12 and Class B has range 40. What does this tell you about the two classes? Reasoning
  8. Invent a 7-value data set where the mean and median are equal but no value equals the mean. Open-ended
  9. The mean of 6 numbers is 15. If you remove a 9, what is the mean of the remaining 5 numbers? Multi-step
  10. A teacher reports the "average" homework time is 30 minutes, but most students did 15 minutes. Which measure of center was probably used, and how could a few large values cause this? Reasoning

Stretch Investigation

Real-world application: Survey at least 15 classmates with the statistical question "How many hours do you spend on homework each week?" Record the data, then compute the mean, median, mode, and range. Build a dot plot. Finally, write three conclusions and state which measure of center best summarizes your class, justifying your choice.

Answer Key

  1. Current total 4+6+6+8+11 = 35; for mean 7 over 6 values need total 42; add 42 − 35 = 7.
  2. Total needed 88 × 5 = 440; known 90+85+92+80 = 347; fifth = 440 − 347 = 93.
  3. The mean — it uses every value, so a large outlier pulls it up; the median only depends on position.
  4. Answers vary, e.g., {10,10,10,10,10} or {8,9,10,11,12} (median/mode 10 needs repeats — e.g., {6,10,10,10,14}).
  5. Mean = 449 ÷ 6 ≈ 74.8; median = (72+73)÷2 = 72.5; median is better because 90 is an outlier.
  6. 4 + 10 + 6 = 20 data points; exact mean cannot be found — only the interval each value falls in is known.
  7. Same average but Class B's scores are far more spread out (more variation/inconsistency).
  8. Answers vary, e.g., {1,2,3,4,5,9,11}: mean = 5, median = 4 — adjust so they match without a 5, e.g., {1,2,3,7,7,8,8}: mean = median = 5.14… accept any valid set.
  9. Total 6 × 15 = 90; remove 9 → 81; new mean 81 ÷ 5 = 16.2.
  10. The mean was likely used; a few students with very long times raise the mean above the typical (median) value.
  11. Stretch: answers vary; full credit requires correct mean/median/mode/range, a dot plot, and a justified choice of center.