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Statistics · Quick Reference
Histograms Cheat Sheet
In one line: a histogram displays the distribution of numeric data by grouping values into intervals (bins) and showing how many data points fall into each — revealing the overall shape of the data.
Key Ideas
1Bins (Class Intervals). Ranges that divide the data into groups, such as 0-10, 10-20, 20-30. Each bar's height shows how many values fall in that bin.
2Histogram vs. Bar Chart. A histogram is for continuous numeric data with no gaps between bars (since bins are adjacent ranges); a bar chart is for categorical data, and bars can have gaps.
3Frequency. The count of data points falling within each bin, shown by the height of each bar.
4Shape of a Distribution. Histograms reveal whether data is symmetric, skewed left, skewed right, or has multiple peaks (bimodal).
5Choosing Bin Width. Too few bins can hide important detail; too many can make the shape look noisy. A reasonable bin width balances clarity and detail.
Worked Examples
Data (test scores): 55, 62, 68, 71, 75, 78, 82, 85, 90, 95. Using bins of width 10 (50-60, 60-70, ...), find the frequency for the 70-80 bin.
Frequency = 3
A histogram has most of its bars concentrated on the left with a long tail extending to the right. Describe this distribution's skew.
This distribution is right-skewed (positively skewed)
Explain why histogram bars touch each other but bar chart bars do not.
Histograms show continuous adjacent intervals, while bar charts show separate, unrelated categories
Practice Yourself
What is a 'bin' in a histogram?
A range of values used to group data for counting frequency
What does the height of a histogram bar represent?
The frequency of data points in that bin
If a histogram's tail extends to the left, how is it skewed?
Left-skewed (negatively skewed)
Why don't histogram bars have gaps between them?
Because the bins represent continuous, adjoining ranges of data