Frequency Distributions and Histograms

GRE Quantitative · Axiom Academy

LESSON Frequency Distributions and Histograms How 200 raw scores become a table of counts, the table becomes the GRE's bar chart, and the chart still yields statistics. A frequency distribution groups data values into intervals (called bins or classes ) and counts how many data points fall into each bin. Below, all 200 test scores sit as an unreadable swarm above the score axis. Split the axis into four equal-width bins — 60–69, 70–79, 80–89, 90–99 — and every score falls into exactly one. Press play to watch the dataset sort itself; the instant a score lands, its bin's frequency ticks up by one. The finished table reads the shape and spread of all 200 scores at a glance — far more useful than the raw list: 2. The Histogram Is the Table, Drawn A histogram is the frequency table, drawn: one bar per bin, and each bar's height equals the frequency of its bin — nothing is rescaled or smoothed. Press play and watch the four bars rise left to right to their true heights (12, 38, 85, 65), so you can see the proportions land in real time. A few things you can read off any histogram at a glance: The tallest bar — here 80–89, with frequency 85. That's the single most common score range in the data. A longer tail on one side signals skew. Here the bars fall away more gradually toward the low scores — a longer left tail, so this distribution is mildly left-skewed. From the lower edge of the first bin (60) to the upper edge of the last bin (99) — the full span the bars cover.

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