A frequency distribution lists each value (or each interval of values) alongside how many times it occurs. The GRE hands you these as tables, histograms or dot plots and asks you to pull out a count, a proportion, or a summary statistic. Two derived columns do most of the work: relative frequency (a value’s count divided by the total, i.e. its share of the data) and cumulative frequency (the running total, which answers "how many are at or below this value?"). To find the mean from a grouped table, weight each value by its frequency: Σ(value × frequency) ÷ Σ(frequency) — do not average the distinct values, or you throw away how common each one is. The median is the value whose cumulative frequency first reaches half the total. Read the axis labels carefully: a histogram bar’s height is a count, not a value.
✅ Solved examples
1. A quiz was marked out of 5. Scores: value 2 → 4 students, 3 → 6 students, 4 → 8 students, 5 → 2 students. How many students took the quiz, and what fraction scored a 4?
Total = 4 + 6 + 8 + 2 = 20 students. Scored a 4: 8 of 20 = 8/20 = 2/5 = 40%.
2. Using the same table (2→4, 3→6, 4→8, 5→2), find the mean score.
3. For the same 20 students, find the median score.
The median is the average of the 10th and 11th values. Cumulative counts: ≤2 is 4, ≤3 is 10, ≤4 is 18. So the 10th value is 3 and the 11th value is 4. Median = (3 + 4)/2 = 3.5.
4. Quantitative Comparison. A histogram shows ages grouped as 10–19 (5 people), 20–29 (12 people), 30–39 (8 people). Quantity A: the number of people under 30. Quantity B: 20. Which is greater?
Under 30 means the first two bars: 5 + 12 = 17. Quantity B is 20, and 17 < 20, so Quantity B is greater. (You cannot see exact ages inside a bar, but "under 30" lines up with a bar boundary, so the count is exact.)
✏️ Practice — try these, take hints as needed
1. Counts: value 1 → 3, 2 → 5, 3 → 7, 4 → 5. What fraction of the data equals 3?
Add all frequencies for the total.
Total = 3 + 5 + 7 + 5.
Then 7 divided by that total.
7/20 = 35%
2. For counts 1→3, 2→5, 3→7, 4→5, find the mean.
Multiply each value by its frequency.
Σ(value × freq) = 3 + 10 + 21 + 20.
Divide 54 by 20.
2.7
3. A table shows daily rainfall (mm): 0 → 12 days, 1 → 9 days, 2 → 6 days, 3 → 3 days. On how many days did it rain at all?
"Rained at all" means 1 mm or more.
Add the last three frequencies.
9 + 6 + 3.
18 days
4. For the rainfall table (0→12, 1→9, 2→6, 3→3), what is the modal rainfall?
The mode is the most frequent value.
Compare the frequencies, not the values.
The largest frequency is 12.
0 mm
5. Cumulative-frequency style: of 40 test-takers, 10 scored below 500, 25 scored below 600, 40 scored below 700. How many scored from 500 up to (but not including) 600?
Cumulative counts subtract.
Below 600 minus below 500.
25 − 10.
15 test-takers
📝 Topic test — 8 questions
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