01 Key Concepts
Bins (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.
Histogram 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.
Frequency
The count of data points falling within each bin, shown by the height of each bar.
Shape of a Distribution
Histograms reveal whether data is symmetric, skewed left, skewed right, or has multiple peaks (bimodal).
Choosing 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.
02 Solved Examples
Example 1 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.
- Identify values falling in [70,80): 71, 75, 78.
- Count them.
Answer: Frequency = 3
Example 2 A histogram has most of its bars concentrated on the left with a long tail extending to the right. Describe this distribution's skew.
- A long tail on the right side, with most data bunched on the left, indicates the distribution is 'pulled' to the right.
Answer: This distribution is right-skewed (positively skewed)
Example 3 Explain why histogram bars touch each other but bar chart bars do not.
- Histogram bins represent continuous, adjoining ranges of numeric data, so there's no natural gap between them.
- Bar charts represent separate categories, which are naturally distinct from one another.
Answer: Histograms show continuous adjacent intervals, while bar charts show separate, unrelated categories
03 Practice Questions
1What is a 'bin' in a histogram?
A range of values used to group data for counting frequency
2What does the height of a histogram bar represent?
The frequency of data points in that bin
3If a histogram's tail extends to the left, how is it skewed?
Left-skewed (negatively skewed)
4Why don't histogram bars have gaps between them?
Because the bins represent continuous, adjoining ranges of data
5Is a histogram used for categorical or numeric data?
Numeric (continuous) data
📄 Histograms — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.