Why Data Analysis Rewards Conceptual Traps Awareness
GRE Data Analysis questions test statistics and probability concepts that are simple in isolation but easy to misapply under time pressure — particularly the difference between mean and median, and the "at least one" probability shortcut that avoids painstaking case-by-case counting.
GRE Data Analysis প্রশ্ন সহজ পরিসংখ্যান ও সম্ভাবনার ধারণা পরীক্ষা করে, কিন্তু সময়ের চাপে ভুল প্রয়োগ সহজ — বিশেষত mean ও median-এর পার্থক্য এবং "at least one" সম্ভাবনা শর্টকাট।
The core method: for "at least one" probability questions, calculate 1 minus the probability that the event never happens at all — this is almost always faster than adding up every individual case where it does happen.
মূল পদ্ধতি: "at least one" প্রশ্নে ১ বিয়োগ করুন কখনো না ঘটার সম্ভাবনা থেকে — এটি প্রায়ই দ্রুততর।
Core Concepts
| Concept | Key Point |
|---|---|
| Mean vs. median | Mean is pulled toward outliers; median is not. A large gap between mean and median signals a skewed distribution with extreme values. |
| Mode | The most frequently occurring value — a data set can have no mode, one mode, or several (bimodal, multimodal). |
| Weighted average | When groups of different sizes are combined, the overall average is pulled closer to the larger group's average, not the simple midpoint of the two averages. |
| "At least one" probability | P(at least one success) = 1 − P(no successes at all). Much faster than summing every individual success scenario. |
| Independent events | P(A and B) = P(A) × P(B) only when A and B don't affect each other (e.g., separate dice rolls, replacement draws). |
| Combinations vs. permutations | Use combinations (order doesn't matter) for committees/groups; use permutations (order matters) for rankings/arrangements. |
Worked Examples
"A small company's five employees earn annual salaries of $30,000, $32,000, $35,000, $38,000, and $500,000 (the owner). Compare the mean and median salary."
"A fair six-sided die is rolled twice. What is the probability of rolling at least one 6?"
Common Mistakes
- Averaging two averages directly: combining a group of 10 with average 80 and a group of 30 with average 90 is NOT 85 — it's a weighted average: (10×80 + 30×90)/40 = 87.5.
- Assuming mean and median are always close: they diverge significantly whenever a data set has extreme outliers or is heavily skewed.
- Multiplying probabilities for dependent events: P(A) × P(B) only works for independent events — drawing without replacement changes the probability of the second event.
- Forgetting to subtract from 1 correctly: "at least one" is the complement of "none," not the complement of "exactly one" — a common source of off-by-one-case errors.
Your Turn
নিচের সমস্যাগুলো সমাধান করুন।
Show the logic
Weighted average = (20×75 + 30×85)/50 = (1500+2550)/50 = 4050/50 = 81 (not the simple midpoint of 80).
Show the logic
P(no heads) = (1/2)³ = 1/8. P(at least one heads) = 1 − 1/8 = 7/8.
Show the logic
Median = (3+4)/2 = 3.5. Mean = (2+3+3+4+5+40)/6 = 57/6 = 9.5. Mean is much larger because the outlier (40) pulls it upward; median is unaffected.
Show the logic
Dependent events: P = (4/52) × (3/51) = 12/2652 = 1/221 (the second probability changes because a card was removed).
Show the logic
8 appears three times, more than any other value. Mode = 8.
This completes the full GRE Strategy Guide series. Return to the Strategy Guides hub or head to the Vocabulary Builder.
সম্পূর্ণ কৌশল গাইড সিরিজ শেষ। হাবে ফিরুন।